Question 49
Points $D$ and $E$ lie on the side $BC$ of an acute-angled triangle $ABC$ such that $\angle DAB = \angle EAC$. Let $\omega$ be a circle whose center lies on the circumcircle of the triangle $ABC$ ($\Gamma$) and is tangent to $AD$ at $A$.
Denote by $A'$ the reflection of point $A$ with respect to $BC$ and the intersection points of $A'E$ and $\omega$ by $K$ and $L$. Prove that either the lines $BK$ and $CL$ or the lines $BL$ and $CK$ meet on $\Gamma$.
Denote by $A'$ the reflection of point $A$ with respect to $BC$ and the intersection points of $A'E$ and $\omega$ by $K$ and $L$. Prove that either the lines $BK$ and $CL$ or the lines $BL$ and $CK$ meet on $\Gamma$.