Senior Kangaroo 2017 Q18

The diagram shows a semicircle with diameter $PQ$ inscribed in a rhombus $ABCD$. The rhombus is tangent to the arc of the semicircle in two places. Points $P$ and $Q$ lie on sides and of the rhombus respectively.

The line of symmetry of the semicircle is coincident with the diagonal $AC$ of the rhombus. It is given that $\angle CBA=60^{\circ}$. The semicircle has radius 10. The area of the rhombus can be written in the form $a\sqrt{b}$ where $a$ and $b$ are integers and $b$ is prime.

What is the value of $ab+a+b$?