Question

The given figure shows sector OAB with centre O and radius 54 cm. Another circle XYZ with centre P, is enclosed by the sector OAB.
If ∠AOB = 60°. Find the area of OXPY.​

Answer 1

Soln:

Given: sector OAB with centre O and radius 54cm.

<AOB=600

OZ=OB=OA=54cm

Construction: join O and P.

Let XP=r, then OP=54-r

In ΔOXP right angled at X,

<XOP=300

Sin300=XP/OP=r/54-r=1/2 then r=18cm-----------(1)

OP=54-18=36cm

So,XP2+OX2=OP2

182+OX2=362 => OX=18√3cm---------------(2)

Area of OXPY quadrilateral=2xarea of ΔOXP

=2x ½ x 18√3 x 18 = 561.2cm(ans.)

#Hope it helps!!