Question 65
In the triangle $ABC$, the incircle is tangent to the sides $AB$ and $AC$ in $D$ and $E$, respectively. The line $DE$ meets the circumcircle in $P$ and $Q$, with $P$ on the minor arc $AB$ and $Q$ on the minor arc $AC$. It is known that $P$ is the midpoint of $AB$. Find $A$ and the ratio $\frac{PQ}{BC}$.