Question 95
Let $\Gamma$ be the circumcircle of a triangle $ABC$, and let $D$ and $E$ be two points different from the vertices on the sides $AB$ and $AC$, respectively. Let $A'$ be the second point where $\Gamma$ intersects the bisector of the angle $\angle BAC$, and let $P$ and $Q$ be the second points where $\Gamma$ intersects the lines $A'D$ and $A'E$, respectively. Let $R$ and $S$ be the second points of intersection of the line $AA'$ and the circumcircles of the triangles $APD$ and $AQE$, respectively. Show that the lines $DS, ER$ and the tangent line to $\Gamma$ through $A$ are concurrent.