SEAMO X 2022 — Paper E — Grade 9–10 Question 4

In triangle $ABC$, $AB=9$, $BC=8$, $CA=7$. The bisector of $\angle BAC$ meets $BC$ at $D$. A circle through $A$, tangent to $BC$ at $D$, meets $AB$ again at $X$ and $AC$ again at $Y$. Find $XY$.