Τρίτη, 17 Οκτωβρίου 2017

2005 IMO Shortlist G3

Let $ABCD$ be a parallelogram. A variable line $l$ passing through the point $A$ intersects the rays $BC$ and $DC$ at points $X$ and $Y$ , respectively. Let $K$ and $L$ be the centres of the excircles of triangles $ABX$ and $ADY$ , touching the sides $BX$ and $DY$ , respectively. Prove that the size of angle $KCL$ does not depend on the choice of the line $ l$.

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