KöMaL problem A, 2023

Geometry Difficulty 8.0 Shortlist Prove it Hungary

The inscribed circle of triangle $ABC$ is tangent to sides $BC$ , $AC$ and $AB$ at points $D$ , $E$ and $F$ , respectively. Let $E'$ be the reflection of point $E$ across line $DF$ , and $F'$ be the reflection of point $F$ across line $DE$ . Let line $EF$ intersect the circumcircle of triangle $AE'F'$ at points $X$ and $Y$ . Prove that $DX=DY$ .

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