Question 13
Let $ABC$ be a triangle with $AB \lt AC$. On the angle bisector of $\angle BAC$, two points $X$ and $Y$ are marked such that $X$ is between $A$ and $Y$, and $BX$ is parallel to $CY$. Let $Z$ be the reflection of $X$ with respect to $BC$. Let $P$ be the point of intersection of lines $YZ$ and $BC$. If lines $BY$ and $CX$ intersect at $K$, prove that $KA = KP$.