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The interceptions of the A-midline on the incircle

Source: Tuymaada 2008, Senior League, First Day, Problem 3.

July 17, 2008
geometrygeometric transformationreflectionincentercircumcirclegeometry proposed

Problem Statement

Point I1 I_1 is the reflection of incentre I I of triangle ABC ABC across the side BC BC. The circumcircle of BCI1 BCI_1 intersects the line II1 II_1 again at point P P. It is known that P P lies outside the incircle of the triangle ABC ABC. Two tangents drawn from P P to the latter circle touch it at points X X and Y Y. Prove that the line XY XY contains a medial line of the triangle ABC ABC. Author: L. Emelyanov
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