ITOT 44 Spring 2023 · THPT · A (Advanced) Question 2

Triangle $ABC$ has perimeter1. Its $A$-excircle touches $BC$ and the extensions of $AB,AC$ along rays $AB,AC$ at $P,Q$, respectively. The line through the midpoints of $AB,AC$ meets the circumcircle of $APQ$ at $X,Y$. Find $XY$.