Question 124
Let $A B \Gamma$ be an acute angled triangle with circumcircle $\omega$. A circle $\gamma$ with center $A$ intersects the arc $AB$ of the circle $\omega$, not containing $\Gamma$, at point $\Delta$ and the arc $A\Gamma$, not containing $B$, at point $E$. We suppose that the point of intersection $K$ of the lines $BE$ and $\Gamma\Delta$ belongs to the $\gamma$. Prove that the line $AK$ is perpendicular to the line $B\Gamma$.