Finding the radius with chord length

Question

I'm struggling to find the radius of the circle in the image (the only other given length is the length between B and the right angle below, which is 5). Is it even possible to get the radius without knowing any other dimensions? Or is there a way to find it? I've tried to use Pythagoras but without knowing the length of the side of the triangle going towards O, it was hard to find it.

Answer 1

There is no way to find $\theta$ or the radius from the given data. To see why, imagine to move point $P$ to the left on the horizontal line and let $O$ be the center of circle $ABP$: all given lengths would stay the same, but $r$ and $\theta$ would change.