2017 OIM Problems/Problem 2

Problem

Let $ABC$ be a right triangle and $\Gamma$ its circumcircle. Let $D$ be a point on the segment $BC$, distinct from $B$ and $C$, and let $M$ be the midpoint of $AD$. The line perpendicular to $AB$ passing through $D$ cuts $AB$ at $E$ and $\Gamma$ at $F$, with point $D$ between $E$ and $F$. The lines $FC$ and $EM$ intersect at the point $X$. If $\angle DAE = \angle AFE$, show that the line $AX$ is tangent to $\Gamma$.

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

Solution

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See also

OIM Problems and Solutions