## Τρίτη, 17 Οκτωβρίου 2017

### 2005 IMO Shortlist G1

In a triangle $ABC$ satisfying $AB + BC = 3AC$ the incircle has centre $I$ and touches the sides $AB$ and $BC$ at $D$ and $E$, respectively. Let $K$ and $L$ be the symmetric points of $D$ and $E$ with respect to $I$. Prove that the quadrilateral $ACKL$ is cyclic.

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