What's the radius?












15














I have a book of puzzles from 1972 with the pretentious title, "Games for the Superintelligent" by James Fixx. One puzzle had me thinking for a couple of days:
ge
I drew it out, thought about different ways of attacking it, and eventually gave up and looked up the answer in the back of the book.
See if you can do better than me and figure out the answer on your own!










share|improve this question









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  • Welcome to Puzzling :D
    – ABcDexter
    Dec 23 at 20:50






  • 1




    I feel like this should go on Math.SE. It's just elementary math, rather than a "puzzle".
    – Hugh
    Dec 23 at 21:24






  • 2




    Fun trivia*: Richard Feynman was stumped by a similar problem! (*source: It's a bit of telephone game, as the source is Walter Bender’s webpage which shares a story told by Oliver Selfridge: web.media.mit.edu/~walter/MAS-A12/week11.html)
    – Presh
    Dec 24 at 9:19






  • 1




    This was a lot of fun. I sat down with my wife for ten minutes trying to crack this. We ended up trying to rewrite things in terms of the usual polar coordinates and facepalmed when the answer spilled out.
    – user1717828
    Dec 24 at 18:04










  • That was a great puzzle! (Are the other puzzles in the book just as fun? I am going to look for it)
    – BruceWayne
    Dec 24 at 23:31
















15














I have a book of puzzles from 1972 with the pretentious title, "Games for the Superintelligent" by James Fixx. One puzzle had me thinking for a couple of days:
ge
I drew it out, thought about different ways of attacking it, and eventually gave up and looked up the answer in the back of the book.
See if you can do better than me and figure out the answer on your own!










share|improve this question









New contributor




WhiteHotLoveTiger is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Welcome to Puzzling :D
    – ABcDexter
    Dec 23 at 20:50






  • 1




    I feel like this should go on Math.SE. It's just elementary math, rather than a "puzzle".
    – Hugh
    Dec 23 at 21:24






  • 2




    Fun trivia*: Richard Feynman was stumped by a similar problem! (*source: It's a bit of telephone game, as the source is Walter Bender’s webpage which shares a story told by Oliver Selfridge: web.media.mit.edu/~walter/MAS-A12/week11.html)
    – Presh
    Dec 24 at 9:19






  • 1




    This was a lot of fun. I sat down with my wife for ten minutes trying to crack this. We ended up trying to rewrite things in terms of the usual polar coordinates and facepalmed when the answer spilled out.
    – user1717828
    Dec 24 at 18:04










  • That was a great puzzle! (Are the other puzzles in the book just as fun? I am going to look for it)
    – BruceWayne
    Dec 24 at 23:31














15












15








15


3





I have a book of puzzles from 1972 with the pretentious title, "Games for the Superintelligent" by James Fixx. One puzzle had me thinking for a couple of days:
ge
I drew it out, thought about different ways of attacking it, and eventually gave up and looked up the answer in the back of the book.
See if you can do better than me and figure out the answer on your own!










share|improve this question









New contributor




WhiteHotLoveTiger is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I have a book of puzzles from 1972 with the pretentious title, "Games for the Superintelligent" by James Fixx. One puzzle had me thinking for a couple of days:
ge
I drew it out, thought about different ways of attacking it, and eventually gave up and looked up the answer in the back of the book.
See if you can do better than me and figure out the answer on your own!







geometry






share|improve this question









New contributor




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Check out our Code of Conduct.











share|improve this question









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Check out our Code of Conduct.









share|improve this question




share|improve this question








edited Dec 23 at 20:57









ABcDexter

5,00133173




5,00133173






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asked Dec 23 at 19:31









WhiteHotLoveTiger

1815




1815




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  • Welcome to Puzzling :D
    – ABcDexter
    Dec 23 at 20:50






  • 1




    I feel like this should go on Math.SE. It's just elementary math, rather than a "puzzle".
    – Hugh
    Dec 23 at 21:24






  • 2




    Fun trivia*: Richard Feynman was stumped by a similar problem! (*source: It's a bit of telephone game, as the source is Walter Bender’s webpage which shares a story told by Oliver Selfridge: web.media.mit.edu/~walter/MAS-A12/week11.html)
    – Presh
    Dec 24 at 9:19






  • 1




    This was a lot of fun. I sat down with my wife for ten minutes trying to crack this. We ended up trying to rewrite things in terms of the usual polar coordinates and facepalmed when the answer spilled out.
    – user1717828
    Dec 24 at 18:04










  • That was a great puzzle! (Are the other puzzles in the book just as fun? I am going to look for it)
    – BruceWayne
    Dec 24 at 23:31


















  • Welcome to Puzzling :D
    – ABcDexter
    Dec 23 at 20:50






  • 1




    I feel like this should go on Math.SE. It's just elementary math, rather than a "puzzle".
    – Hugh
    Dec 23 at 21:24






  • 2




    Fun trivia*: Richard Feynman was stumped by a similar problem! (*source: It's a bit of telephone game, as the source is Walter Bender’s webpage which shares a story told by Oliver Selfridge: web.media.mit.edu/~walter/MAS-A12/week11.html)
    – Presh
    Dec 24 at 9:19






  • 1




    This was a lot of fun. I sat down with my wife for ten minutes trying to crack this. We ended up trying to rewrite things in terms of the usual polar coordinates and facepalmed when the answer spilled out.
    – user1717828
    Dec 24 at 18:04










  • That was a great puzzle! (Are the other puzzles in the book just as fun? I am going to look for it)
    – BruceWayne
    Dec 24 at 23:31
















Welcome to Puzzling :D
– ABcDexter
Dec 23 at 20:50




Welcome to Puzzling :D
– ABcDexter
Dec 23 at 20:50




1




1




I feel like this should go on Math.SE. It's just elementary math, rather than a "puzzle".
– Hugh
Dec 23 at 21:24




I feel like this should go on Math.SE. It's just elementary math, rather than a "puzzle".
– Hugh
Dec 23 at 21:24




2




2




Fun trivia*: Richard Feynman was stumped by a similar problem! (*source: It's a bit of telephone game, as the source is Walter Bender’s webpage which shares a story told by Oliver Selfridge: web.media.mit.edu/~walter/MAS-A12/week11.html)
– Presh
Dec 24 at 9:19




Fun trivia*: Richard Feynman was stumped by a similar problem! (*source: It's a bit of telephone game, as the source is Walter Bender’s webpage which shares a story told by Oliver Selfridge: web.media.mit.edu/~walter/MAS-A12/week11.html)
– Presh
Dec 24 at 9:19




1




1




This was a lot of fun. I sat down with my wife for ten minutes trying to crack this. We ended up trying to rewrite things in terms of the usual polar coordinates and facepalmed when the answer spilled out.
– user1717828
Dec 24 at 18:04




This was a lot of fun. I sat down with my wife for ten minutes trying to crack this. We ended up trying to rewrite things in terms of the usual polar coordinates and facepalmed when the answer spilled out.
– user1717828
Dec 24 at 18:04












That was a great puzzle! (Are the other puzzles in the book just as fun? I am going to look for it)
– BruceWayne
Dec 24 at 23:31




That was a great puzzle! (Are the other puzzles in the book just as fun? I am going to look for it)
– BruceWayne
Dec 24 at 23:31










4 Answers
4






active

oldest

votes


















24














Is it:




8 inches. Because the other diagonal of the same rectangle is also $8^"$, which coincidentally, is also the radius of the circle.







share|improve this answer



















  • 2




    "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
    – hkBst
    Dec 25 at 9:50



















4














Lol! If you're using Pythagorus you're doing it wrong :-)




8" Draw a diagonal line between the other 2 corners of the rectangle. You'll immediately see the answer and then you'll be kicking yourself!







share|improve this answer








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    0














    So,
    A right-angled square rests plumb atop the diameter of a circle. The distance from the square edge to the circle’s edge is 3”, so then the radius of the circle would be the 5” of the square arm, which is at right angles at two arms spread from opposite the hypotenuse in a meeting of two mirrored triangles; added to the 3” of extension to the circle’s edge -resulting in a radius measurement of a combined(square arm+extension to circle edge) 8”.
    I solved this visually first, but then challenged myself to articulate. I still feel rocky about the explanation and should have drawn it out to clarify as I have been taught instinctual to “show my work.”






    share|improve this answer








    New contributor




    Adam Borchardt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      -1















      Radius.......

      From the word we can understood that it means that half of any object...

      But your subject is geometry so:

      If we consider a circle it is the half of the diameter of the circle...

      So, according to your question...

      Your answer is 8 inches. Because the rectangle with the 8′′ marked other diagonal is the radius, and this is also 8′′ long







      share|improve this answer










      New contributor




      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.














      • 2




        The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
        – Acccumulation
        Dec 24 at 16:10











      Your Answer





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      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      24














      Is it:




      8 inches. Because the other diagonal of the same rectangle is also $8^"$, which coincidentally, is also the radius of the circle.







      share|improve this answer



















      • 2




        "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
        – hkBst
        Dec 25 at 9:50
















      24














      Is it:




      8 inches. Because the other diagonal of the same rectangle is also $8^"$, which coincidentally, is also the radius of the circle.







      share|improve this answer



















      • 2




        "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
        – hkBst
        Dec 25 at 9:50














      24












      24








      24






      Is it:




      8 inches. Because the other diagonal of the same rectangle is also $8^"$, which coincidentally, is also the radius of the circle.







      share|improve this answer














      Is it:




      8 inches. Because the other diagonal of the same rectangle is also $8^"$, which coincidentally, is also the radius of the circle.








      share|improve this answer














      share|improve this answer



      share|improve this answer








      edited 2 days ago









      Benjamin Lee

      33




      33










      answered Dec 23 at 19:43









      JonMark Perry

      17.4k63483




      17.4k63483








      • 2




        "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
        – hkBst
        Dec 25 at 9:50














      • 2




        "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
        – hkBst
        Dec 25 at 9:50








      2




      2




      "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
      – hkBst
      Dec 25 at 9:50




      "the rectangle with the 8′′ marked other diagonal is the radius", so basically "the rectangle ... is the radius"? That seem ungrammatical to me.
      – hkBst
      Dec 25 at 9:50











      4














      Lol! If you're using Pythagorus you're doing it wrong :-)




      8" Draw a diagonal line between the other 2 corners of the rectangle. You'll immediately see the answer and then you'll be kicking yourself!







      share|improve this answer








      New contributor




      Gazzer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.























        4














        Lol! If you're using Pythagorus you're doing it wrong :-)




        8" Draw a diagonal line between the other 2 corners of the rectangle. You'll immediately see the answer and then you'll be kicking yourself!







        share|improve this answer








        New contributor




        Gazzer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
        Check out our Code of Conduct.





















          4












          4








          4






          Lol! If you're using Pythagorus you're doing it wrong :-)




          8" Draw a diagonal line between the other 2 corners of the rectangle. You'll immediately see the answer and then you'll be kicking yourself!







          share|improve this answer








          New contributor




          Gazzer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.









          Lol! If you're using Pythagorus you're doing it wrong :-)




          8" Draw a diagonal line between the other 2 corners of the rectangle. You'll immediately see the answer and then you'll be kicking yourself!








          share|improve this answer








          New contributor




          Gazzer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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          share|improve this answer



          share|improve this answer






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          answered Dec 24 at 10:25









          Gazzer

          1411




          1411




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              0














              So,
              A right-angled square rests plumb atop the diameter of a circle. The distance from the square edge to the circle’s edge is 3”, so then the radius of the circle would be the 5” of the square arm, which is at right angles at two arms spread from opposite the hypotenuse in a meeting of two mirrored triangles; added to the 3” of extension to the circle’s edge -resulting in a radius measurement of a combined(square arm+extension to circle edge) 8”.
              I solved this visually first, but then challenged myself to articulate. I still feel rocky about the explanation and should have drawn it out to clarify as I have been taught instinctual to “show my work.”






              share|improve this answer








              New contributor




              Adam Borchardt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.























                0














                So,
                A right-angled square rests plumb atop the diameter of a circle. The distance from the square edge to the circle’s edge is 3”, so then the radius of the circle would be the 5” of the square arm, which is at right angles at two arms spread from opposite the hypotenuse in a meeting of two mirrored triangles; added to the 3” of extension to the circle’s edge -resulting in a radius measurement of a combined(square arm+extension to circle edge) 8”.
                I solved this visually first, but then challenged myself to articulate. I still feel rocky about the explanation and should have drawn it out to clarify as I have been taught instinctual to “show my work.”






                share|improve this answer








                New contributor




                Adam Borchardt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.





















                  0












                  0








                  0






                  So,
                  A right-angled square rests plumb atop the diameter of a circle. The distance from the square edge to the circle’s edge is 3”, so then the radius of the circle would be the 5” of the square arm, which is at right angles at two arms spread from opposite the hypotenuse in a meeting of two mirrored triangles; added to the 3” of extension to the circle’s edge -resulting in a radius measurement of a combined(square arm+extension to circle edge) 8”.
                  I solved this visually first, but then challenged myself to articulate. I still feel rocky about the explanation and should have drawn it out to clarify as I have been taught instinctual to “show my work.”






                  share|improve this answer








                  New contributor




                  Adam Borchardt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  So,
                  A right-angled square rests plumb atop the diameter of a circle. The distance from the square edge to the circle’s edge is 3”, so then the radius of the circle would be the 5” of the square arm, which is at right angles at two arms spread from opposite the hypotenuse in a meeting of two mirrored triangles; added to the 3” of extension to the circle’s edge -resulting in a radius measurement of a combined(square arm+extension to circle edge) 8”.
                  I solved this visually first, but then challenged myself to articulate. I still feel rocky about the explanation and should have drawn it out to clarify as I have been taught instinctual to “show my work.”







                  share|improve this answer








                  New contributor




                  Adam Borchardt is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  share|improve this answer



                  share|improve this answer






                  New contributor




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                  answered yesterday









                  Adam Borchardt

                  1




                  1




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                  New contributor





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                      -1















                      Radius.......

                      From the word we can understood that it means that half of any object...

                      But your subject is geometry so:

                      If we consider a circle it is the half of the diameter of the circle...

                      So, according to your question...

                      Your answer is 8 inches. Because the rectangle with the 8′′ marked other diagonal is the radius, and this is also 8′′ long







                      share|improve this answer










                      New contributor




                      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.














                      • 2




                        The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
                        – Acccumulation
                        Dec 24 at 16:10
















                      -1















                      Radius.......

                      From the word we can understood that it means that half of any object...

                      But your subject is geometry so:

                      If we consider a circle it is the half of the diameter of the circle...

                      So, according to your question...

                      Your answer is 8 inches. Because the rectangle with the 8′′ marked other diagonal is the radius, and this is also 8′′ long







                      share|improve this answer










                      New contributor




                      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.














                      • 2




                        The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
                        – Acccumulation
                        Dec 24 at 16:10














                      -1












                      -1








                      -1







                      Radius.......

                      From the word we can understood that it means that half of any object...

                      But your subject is geometry so:

                      If we consider a circle it is the half of the diameter of the circle...

                      So, according to your question...

                      Your answer is 8 inches. Because the rectangle with the 8′′ marked other diagonal is the radius, and this is also 8′′ long







                      share|improve this answer










                      New contributor




                      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.










                      Radius.......

                      From the word we can understood that it means that half of any object...

                      But your subject is geometry so:

                      If we consider a circle it is the half of the diameter of the circle...

                      So, according to your question...

                      Your answer is 8 inches. Because the rectangle with the 8′′ marked other diagonal is the radius, and this is also 8′′ long








                      share|improve this answer










                      New contributor




                      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.









                      share|improve this answer



                      share|improve this answer








                      edited Dec 24 at 17:51









                      Ahmed Ashour

                      948212




                      948212






                      New contributor




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                      answered Dec 24 at 14:08









                      arka

                      1




                      1




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                      New contributor





                      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.






                      arka is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.








                      • 2




                        The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
                        – Acccumulation
                        Dec 24 at 16:10














                      • 2




                        The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
                        – Acccumulation
                        Dec 24 at 16:10








                      2




                      2




                      The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
                      – Acccumulation
                      Dec 24 at 16:10




                      The first three fourths of your question is just regurgitating definitions (and not even the correct one, at first: I'm not aware of any definition of "radius" being "half of any object), and the rest is just repeating what other answers have said.
                      – Acccumulation
                      Dec 24 at 16:10










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