Question 33
Let $\triangle AB\Gamma$ with $AB \lt A\Gamma \lt B\Gamma$ be a triangle inscribed in a circle $c$ with center $O$. Let $\Delta$ be the diametrically opposite to $A$ and $c_1$ is a circle which has center $K$ on $B\Delta$ and passes through $B$ and $\Gamma$. If $c_1$ meets $A\Gamma$ at the point $E$, prove that the circumcircle of $BKE$, let it be $c_2$, is tangent to $c$.