CBSE Class 10 Maths (Standard) 2016 · Paper 30/1 · Question 30

In Fig. 9, is shown a sector $OAP$ of a circle with centre $O$, containing $\angle \theta$. $AB$ is perpendicular to the radius $OA$ and meets $OP$ produced at $B$. Prove that the perimeter of shaded region is $r\left[\tan \theta +\sec \theta +\frac{\pi \theta }{180}-1\right]$.