Question 49
Let $ABC$ be an equilateral triangle with side length $8$. Let $X$ be on side $AB$ so that $AX = 5$ and $Y$ be on side $AC$ so that $AY = 3$. Let $Z$ be on side $BC$ so that $AZ$, $BY$, $CX$ are concurrent. Let $ZX$, $ZY$ intersect the circumcircle of $AXY$ again at $P$, $Q$ respectively. Let $XQ$ and $YP$ intersect at $K$. Compute $KX \cdot KQ$.