Question 2
In triangle $ABC$, $\angle ABC = 50^{\circ}$ and $\angle ACB = 70^{\circ}$. Let $D$ be the midpoint of side $BC$. A circle is tangent to $BC$ at $B$ and is also tangent to segment $AD$; this circle intersects $AB$ again at $P$. Another circle is tangent to $BC$ at $C$ and is also tangent to segment $AD$; this circle intersects $AC$ again at $Q$. Find $\angle APQ$ (in degrees).