XYZ Triangle

Given $\triangle ABC$ with circumcircle $\Gamma$ , let $X$ be the midpoint of arc $BAC$ and let $Y, Z$ be the tangency points of the $B, C$ excircle with $AC, AB$ , respectively. If $XY = 7, YZ = 8$ find $[XYZ]$ . The answer can be expressed as $p\sqrt{q}$ where $p,q$ are positive integers and $q$ is square free. As your answer, submit $p+q$ .