interesting geometry problem
Source:
April 28, 2008
geometrygeometry proposed
Problem Statement
Let ABCD be a square and K
be a circle with diameter AB. For an
arbitrary point P on side CD, segments AP and BP meet K
again at
points M and N, respectively, and lines DM and CN meet at point Q.
Prove that Q lies on the circle K
and that AQ : QB = DP : PC.