wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> medium >> ABCD is a cyclic quadrilateral
        
(Message started by: tony123 on Nov 19th, 2007, 9:34am)
Title: ABCD is a cyclic quadrilateral
Post by tony123 on Nov 19th, 2007, 9:34am
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.
Title: Re: ABCD is a cyclic quadrilateral
Post by pex on Nov 19th, 2007, 9:37am

on 11/19/07 at 09:34:11, 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?
Title: Re: ABCD is a cyclic quadrilateral
Post by towr on Nov 19th, 2007, 10:00am
≠ is http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/ne.gif

[edit]It seems to be problem ten of http://cemc.uwaterloo.ca/english/contests/past_contest/1999/euclid.pdf[/edit]
Title: Re: ABCD is a cyclic quadrilateral
Post by thinktank on Nov 20th, 2007, 7:48am
The least value of d I think is [hide]9[/hide]

The proof for d not being a prime is also not that difficult...use the equation [hide]d(d-b)=2a2[/hide]
Title: Re: ABCD is a cyclic quadrilateral
Post by pex on Nov 20th, 2007, 8:26am

on 11/20/07 at 07:48:23, thinktank wrote:
The least value of d I think is [hide]9[/hide]

The proof for d not being a prime is also not that difficult...use the equation [hide]d(d-b)=2a2[/hide]

Aha... but isn't [hide]8*(8-7)=2*22[/hide]?


Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board