A square ABCD is incribed in a circle. Prove that the distances between a point P on the circumference to the four vertices of the square canīt all be rational numbers.

(In reply to A start by Patrick)

If PA, PB PC and PD are all rational, then the product of any two is also rational...  For example cos(G) and sin(G) must both be rational from multiplying PA PC and PB PD.

Now all we have to do is find how this leads to a contradiction.

Edited on December 13, 2005, 11:01 am

Posted by goFish on 2005-12-13 10:52:03