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DE intersects AB,AC at touchpoints of ABC wiht it's incircle

Source: 2011 Portugal p5

October 10, 2020
geometryincircleprojectionsAngle Bisectors

Problem Statement

Let [ABC][ABC] be a triangle, DD be the orthogonal projection of BB on the bisector of ∠ACB\angle ACB and EE the orthogonal projection of CC on the bisector of ∠ABC\angle ABC . Prove that DEDE intersects the sides [AB][AB] and [AC][AC] at the touchpoints of the circle inscribed in the triangle [ABC][ABC].
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