Chapter 8.3, Problem 60AYU

Rods and Pistons Rod $OA$ rotates about the fixed point $O$ so that point $A$ travels on a circle of radius $r$. Connected to point $A$ is another rod $AB$ of length $L>2r$, and point $B$ is connected to a piston. See the figure. Show that the distance $x$ between point $O$ and point $B$ is given by

$x=r\cos \theta +\sqrt{r^2{\cos }^2\theta +L^2-r^2}$

where $\theta$ is the angle of rotation of rod $OA$.