There are two circles intersecting each other. Another smaller circle with centre O, is lying between the common region of the two larger circles.

Question

There are two circles intersecting each other. Another smaller circle with center O, is lying between the common region of the two larger circles. Centers of the circle (i.e., A, O and B) are lying on a straight line. AB = 16 cm and the radii of the larger circles are 10 cm each. What is the area of the smaller circle?

(a) 4π cm² 

(b) 2π cm² 

(c) \(\frac{4}{π}\) cm² 

(d) \(\frac{π}{4}\) cm²

Answer 1

Answer : (a) 4π cm² 

Given figure: 

AB = 16 cm 

AQ = 10 cm

AO = \(\frac{AB}{2}\) = 8 cm

∴ OQ = AQ – AO = 10 cm – 8 cm = 2 cm

∴ Area of smaller circle with centre O = π × (2)² 

= 4π cm²