MathDB
Iran(3rd round)2009

Source: Problem 4 Geometry

September 13, 2009
geometryincenterpower of a pointradical axisgeometry unsolved

Problem Statement

4-Point P P is taken on the segment BC BC of the scalene triangle ABC ABC such that AP≠AB,AP≠AC AP \neq AB,AP \neq AC.l1,l2 l_1,l_2 are the incenters of triangles ABP,ACP ABP,ACP respectively. circles W1,W2 W_1,W_2 are drawn centered at l1,l2 l_1,l_2 and with radius equal to l1P,l2P l_1P,l_2P,respectively. W1,W2 W_1,W_2 intersects at P P and Q Q. W1 W_1 intersects AB AB and BC BC at Y_1( \mbox{the intersection closer to B}) and X1 X_1,respectively. W2 W_2 intersects AC AC and BC BC at Y_2(\mbox{the intersection closer to C}) and X2 X_2,respectively.PROVE THE CONCURRENCY OF PQ,X1Y1,X2Y2 PQ,X_1Y_1,X_2Y_2.
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