MathDB
Similar triangles

Source: VNTST 2024 Day 1 Problem 3

March 26, 2024
geometrysimilar triangles

Problem Statement

Let ABCABC be an acute scalene triangle. Incircle of ABCABC touches BC,CA,ABBC,CA,AB at D,E,FD,E,F respectively. Let X,Y,ZX,Y,Z be feet the altitudes of from A,B,CA,B,C to the sides BC,CA,ABBC,CA,AB respectively. Let A′,B′,C′A',B',C' be the reflections of X,Y,ZX,Y,Z in EF,FD,DEEF,FD,DE respectively. Prove that triangles ABCABC and A′B′C′A'B'C' are similar.
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