MathDB
Geometry

Source: Poland - Second Round P3

February 8, 2020
geometryparallelogram

Problem Statement

Let MM be the midpoint of the side BCBC of a acute triangle ABCABC. Incircle of the triangle ABMABM is tangent to the side ABAB at the point DD. Incircle of the triangle ACMACM is tangent to the side ACAC at the point EE. Let FF be the such point, that the quadrilateral DMEFDMEF is a parallelogram. Prove that FF lies on the bisector of ∠BAC\angle BAC.
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