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Concurrent angle bisectors

Source: EGMO 2019 Problem 3

April 9, 2019
geometryEGMO 2019

Problem Statement

Let ABCABC be a triangle such that ∠CAB>∠ABC\angle CAB > \angle ABC, and let II be its incentre. Let DD be the point on segment BCBC such that ∠CAD=∠ABC\angle CAD = \angle ABC. Let ω\omega be the circle tangent to ACAC at AA and passing through II. Let XX be the second point of intersection of ω\omega and the circumcircle of ABCABC. Prove that the angle bisectors of ∠DAB\angle DAB and ∠CXB\angle CXB intersect at a point on line BCBC.
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