MathDB

2

Part of 2023 Balkan MO

Problems(1)

Geometry of BMO 2023

Source: BMO 2023 Problem 2

5/10/2023
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.
United Kingdom
geometryBMO 2023