Problem

Source: Problem 4 Geometry

Tags: geometry, incenter, power of a point, radical axis, geometry unsolved



4-Point P is taken on the segment BC of the scalene triangle ABC such that APAB,APAC.l1,l2 are the incenters of triangles ABP,ACP respectively. circles W1,W2 are drawn centered at l1,l2 and with radius equal to l1P,l2P,respectively. W1,W2 intersects at P and Q. W1 intersects AB and BC at Y1(the intersection closer to B) and X1,respectively. W2 intersects AC and BC at Y2(the intersection closer to C) and X2,respectively.PROVE THE CONCURRENCY OF PQ,X1Y1,X2Y2.