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2017 IGO Advanced P1

Source: 4th Iranian Geometry Olympiad (Advanced) P1

September 15, 2017
geometryIranIGO

Problem Statement

In triangle ABCABC, the incircle, with center II, touches the sides BCBC at point DD. Line DIDI meets ACAC at XX. The tangent line from XX to the incircle (different from ACAC) intersects ABAB at YY. If YIYI and BCBC intersect at point ZZ, prove that AB=BZAB=BZ.
Proposed by Hooman Fattahimoghaddam
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