CAT 2018 Slot 1 QA Question 4: In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectivel

Question

In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectivel

Accepted Answer

The area of sector R with radius 1 cm and central angle 60$\degree$ is
$\dfrac{60}{360} 	imes \pi 	imes 1^{2} = \dfrac{\pi}{6}$
So, the area of triangle OCD is half of this:
Area of triangle OCD $=\dfrac{\pi}{12}$
Let $OC = OD = x$. The angle COD is 60$\degree$.
Area of triangle OCD $=\dfrac{1}{2