Estonian Math Competitions 2006/2007
Source: Finalround Problem 9
July 29, 2008
geometrycircumcirclegeometry unsolved
Problem Statement
A circle passing through the endpoints of the leg AB of an isosceles triangle ABC
intersects the base BC in point P. A line tangent to the circle in point B intersects the circumcircle of ABC in point Q. Prove that P lies on line AQ if and only if AQ and BC are perpendicular.