2022 OIM Problems/Problem 5

Problem

Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $P$ and $Q$ be points on the half-plane defined by $BC$ that contains $A$, such that $BP$ and $CQ$ are tangent to $\Gamma$ and $PB = BC = CQ$. Let $K$ and $L$ be points on the external bisector of $\angle CAB$, such that $BK = BA$ and $CL = CA$. Let $M$ be the point of intersection of lines $PK$ and $QL$. Prove that $MK = ML$.

Solution

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See also

https://sites.google.com/uan.edu.co/oim-2022/inicio