MathNet 2020 — Math Olympiad Vault — Part 01 Question 42

Let $ABC$ be an acute triangle with $AB = AC$, let $D$ be the midpoint of the side $AC$, and let $\gamma$ be the circumcircle of the triangle $ABD$. The tangent of $\gamma$ at $A$ crosses the line $BC$ at $E$. Let $O$ be the circumcentre of the triangle $ABE$. Prove that the midpoint of the segment $AO$ lies on $\gamma$.
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