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BMO Shortlist 2021 G8

Source: BMO Shortlist 2021

May 8, 2022
Balkanshortlist2021geometryside bash

Problem Statement

Let ABCABC be a scalene triangle and let II be its incenter. The projections of II on BC,CABC, CA, and ABAB are D,ED, E and FF respectively. Let KK be the reflection of DD over the line AIAI, and let LL be the second point of intersection of the circumcircles of the triangles BFKBFK and CEKCEK. If 13BC=AC−AB\frac{1}{3} BC = AC - AB, prove that DE=2KLDE = 2KL.
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