Let $P$ and $Q$ be $2$ circles externally touching each other at point $X$. Line segment $AB$ is a direct common tangent to circles $P$ and $Q$ at points $A$ and $B$ respectively. Another common tangent to $P$ and $Q$ at $X$ intersects line $AB$ at a point $Y$. If $BY=10$ units and the radius of $P$ is $9$ units, then the value of the reciprocal of the radius of the circle $Q$ is equal to