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Three concurrent lines related to incircle

Source: Korea National Olympiad 2010 Problem 3

September 9, 2012
geometryincenterinradiustrigonometrycircumcircleangle bisectorpower of a point

Problem Statement

Let I I be the incenter of triangle ABC ABC . The incircle touches BC,CA,AB BC, CA, AB at points P,Q,R P, Q, R . A circle passing through B,C B , C is tangent to the circle II at point X X , a circle passing through C,A C , A is tangent to the circle II at point Y Y , and a circle passing through A,B A , B is tangent to the circle II at point Z Z , respectively. Prove that three lines PX,QY,RZ PX, QY, RZ are concurrent.
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