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Geometry of BMO 2023

Source: BMO 2023 Problem 2

May 10, 2023
geometryBMO 2023

Problem Statement

In triangle ABCABC, the incircle touches sides BC,CA,ABBC,CA,AB at D,E,FD,E,F respectively. Assume there exists a point XX on the line EFEF such that ∠XBC=∠XCB=45∘.\angle{XBC} = \angle{XCB} = 45^{\circ}. Let MM be the midpoint of the arc BCBC on the circumcircle of ABCABC not containing AA. Prove that the line MDMD passes through EE or FF.
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