MathDB

5

Part of 2011 Portugal MO

Problems(1)

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

Source: 2011 Portugal p5

10/10/2020
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].
geometryincircleprojectionsAngle Bisectors