Τρίτη, 17 Οκτωβρίου 2017

2006 IMO Shortlist G2

Let $ABCD$ be a trapezoid with parallel sides $AB > CD$.  Points $K$ and $L$ lie on the line segments $AB$ and $CD$, respectively, so that $AK/KB = DL/LC$. Suppose that there are points $P$ and $Q$ on the line segment $KL$ satisfying $\angle APB = \angle BCD$  and $ \angle CQD = \angle ABC$. Prove that the points $P , Q, B$ and $C$ are concyclic.


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