To two circles r1 and r2, intersecting at points A and B, their common tangent CD is drawn (C and D are tangency points, respectively, point B is closer to line CB than A). Line passing through A , intersects r1 and r2 for second time at points K and L, respectively (A lies between K and L). Lines KC and LD intersect at point P. Prove that PB is the symmedian of triangle KPL. (Yu. Blinkov)
Problem
Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p6
Tags: geometry, symmedian, circles