Question 33
Draw a circle $\gamma$ through point $M$ which is the middle point of the arc $BC$ not containing vertex $A$ and the center $I$ of incircle of the triangle $ABC$. If the circle $\gamma$ intersects side $BC$ in points $D$, $E$ and the lines $MD$, $ME$ intersect the circle $\omega$ in points $P$, $Q$ which are different from $M$ then prove that all possible lines $PQ$ pass through a constant point not depending from circle $\gamma$.