2019 OIM Problems/Problem 4

Problem

Let $ABCD$ be a trapezoid with $AB \parallel CD$ and inscribed in the circle $\Gamma$. Let $P$ and $Q$ be two points on the segment $AB$ ($A, P, Q, B$ are in that order and are different) such that $AP = QB$. Let $E$ and $F$ be the second points of intersection of the lines $CP$ and $CQ$ with $\Gamma$, respectively. The lines $AB$ and $EF$ intersect at $G$. Prove that the line $DG$ is tangent to $\Gamma$.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions