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Incenter and equal angles

Source: Sharygin Geometry Olympiad 2012 - Problem 3

April 28, 2012
geometryincenterperpendicular bisectorangle bisectorgeometry unsolved

Problem Statement

A circle with center II touches sides AB,BC,CAAB,BC,CA of triangle ABCABC in points C1,A1,B1C_{1},A_{1},B_{1}. Lines AI,CI,B1IAI, CI, B_{1}I meet A1C1A_{1}C_{1} in points X,Y,ZX, Y, Z respectively. Prove that ∠YB1Z=∠XB1Z\angle Y B_{1}Z = \angle XB_{1}Z.
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