A convex quadrilateral ABCD has its diagonals perpendicular to each other. The opposite sides AB and CD are not parallel. The perpendicular bisectors of AB and CD meet at P, which lies in the interior of ABCD. Prove that ABCD is cyclic only if triangles ABP and CDP have equal areas
2007-01-01 02:56:25 · 1 answers · asked by Akilesh - Internet Undertaker 7 in Science & Mathematics ➔ Mathematics
Well, I'd rather be able to explain this myself, but it's been too long since I've been in geometry. I remember the basics, but this one's pretty advanced.
I did some solutions on the net for you, though.
http://www.kalva.demon.co.uk/imo/isoln/isoln981.html
http://sms.math.nus.edu.sg/Simo/IMO_Problems%5C98.pdf
The google search I used was:
http://www.google.com/search?sourceid=navclient&ie=UTF-8&rls=DELA,DELA:2005-51,DELA:en&q=Prove+that+ABCD+is+cyclic+only+if+triangles+ABP+and+CDP+have+equal+areas
2007-01-01 04:36:46 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋