Lots of circles and lines
Source: Bosnia and Herzegovina TST 2015 day 1 problem 2
May 16, 2015
geometrycircumcircleperpendicular bisector
Problem Statement
Let be an arbitrary point on side of triangle . Circumcircles of triangles and intersect sides and at points and , respectively. Perpendicular bisector of cuts at point , and line perpendicular to at at point . Lines and intersect at point , and the second point of intersection of circumcircle of triangle and line is . Prove that