In a circle of radius

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

Problem

10\,\text{cm}

, a chord

AB

subtends an angle of

240^{\circ}

at the centre

O

. Solve the following. (i) Determine whether the sector

OAB

is minor or major. State the reason clearly. (ii) Find the area of the sector

OAB

. (Use

\pi = 3.14

.) (iii) Find the area of the other sector formed by

OA

and

OB

. (iv) The minor segment is the region bounded by chord

AB

and the smaller intercepted arc. Calculate the area of this minor segment, given that

\angle AOB

for this segment is

120^{\circ}

. (Use

\sin120^{\circ}=\dfrac{\sqrt{3}}{2}