Question 117
Let $ABC$ be a triangle with $AB = 6$, $AC = 7$, $BC = 8$. Let $I$ be the incenter of $ABC$. Points $Z$ and $Y$ lie on the interior of segments $AB$ and $AC$ respectively such that $YZ$ is tangent to the incircle. Given point $P$ such that
$$
\angle ZPC = \angle YPB = 90^\circ
$$
find the length of $IP$.
$$
\angle ZPC = \angle YPB = 90^\circ
$$
find the length of $IP$.