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wu :: forums    riddles    medium (Moderators: SMQ, Icarus, ThudnBlunder, william wu, Eigenray, towr, Grimbal)    ABCD is a cyclic quadrilateral « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: ABCD is a cyclic quadrilateral  (Read 3179 times) tony123 Junior Member     Posts: 61 ABCD is a cyclic quadrilateral   « on: Nov 19th, 2007, 9:34am » Quote Modify ABCD is a cyclic quadrilateral,  with side AD= d where d is the diameter of the circle. AB= a   BC= a and CD= b If a, b and d are integers a =\= b   (a)prove that d cannot be a prime number          .   (b)determine the minimum value of d.     « Last Edit: Nov 19th, 2007, 1:20pm by tony123 » IP Logged pex Uberpuzzler     Gender: Posts: 880 Re: ABCD is a cyclic quadrilateral   « Reply #1 on: Nov 19th, 2007, 9:37am » Quote Modify on Nov 19th, 2007, 9:34am, tony123 wrote: ABCD is a cyclic quadrilateral,  with side AD= d where d is the diameter of the circle. AB= a   BC= a and CD= b If a, b and d are integers a ≠ b   (a)prove that d cannot be a prime number     .   (b)determine the minimum value of d.   Online Not again... what is ≠ ? And does the "Online" at the end come from wherever you copied it from? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: ABCD is a cyclic quadrilateral   « Reply #2 on: Nov 19th, 2007, 10:00am » Quote Modify ≠ is   [edit]It seems to be problem ten of http://cemc.uwaterloo.ca/english/contests/past_contest/1999/euclid.pdf[/edit] « Last Edit: Nov 19th, 2007, 10:02am by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB thinktank Newbie     Posts: 10 Re: ABCD is a cyclic quadrilateral   « Reply #3 on: Nov 20th, 2007, 7:48am » Quote Modify The least value of d I think is 9   The proof for d not being a prime is also not that difficult...use the equation d(d-b)=2a2 « Last Edit: Nov 20th, 2007, 7:55am by thinktank » IP Logged pex Uberpuzzler     Gender: Posts: 880 Re: ABCD is a cyclic quadrilateral   « Reply #4 on: Nov 20th, 2007, 8:26am » Quote Modify on Nov 20th, 2007, 7:48am, thinktank wrote: The least value of d I think is 9   The proof for d not being a prime is also not that difficult...use the equation d(d-b)=2a2 Aha... but isn't 8*(8-7)=2*22? IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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