In a circle of radius

MATHEMATICS · Multi-part · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

12\,\text{cm}

, radii

OA

OB

and

OC

are drawn so that

\angle AOB = 120^\circ

and

\angle AOC = 60^\circ

, with all three points

A,B,C

on the same side of

OA

. The region bounded by arc

AB

, arc

AC

and chord

BC

is shaded. (i) Find the area of the segment corresponding to arc

AB

. (ii) Find the area of the segment corresponding to arc

AC

. (iii) Determine the area of the shaded region between the two arcs.