MathDB
tangent line to incircle of square wanted

Source: 2021 Francophone MO Seniors p3

April 3, 2021
geometrysquareincircletangentFrancophone

Problem Statement

Let ABCDABCD be a square with incircle Γ\Gamma. Let MM be the midpoint of the segment [CD][CD]. Let P≠BP \neq B be a point on the segment [AB][AB]. Let E≠ME \neq M be the point on Γ\Gamma such that (DP)(DP) and (EM)(EM) are parallel. The lines (CP)(CP) and (AD)(AD) meet each other at FF. Prove that the line (EF)(EF) is tangent to Γ\Gamma
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