Question

the diameter of two circles with Centre A and B are 16 cm and 30 cm respectively if your area of circle with Centre C is equal to the difference of areas of the two circles then find the circumference of the circle with Centre c

Answer 1

Let the radius of circle with centre A, B, C be r1, r2 , r3 respectively.

r1 = 16/2 = 8 cm
r2 = 30/2 = 15 cm
A.T.S.
πr12 + πr22 = πr32
π (r12 + r22) = πr32
64 + 125 = r32
r32 = 189
r3 = 17 cm
Circumference of the circle with centre C = 2πr3
  = 2 x 22/7 x 17
  = 748/7 = 106.85 cm

Answer 2

Area of circle = πr^2,

Let the radius of circle with centre C = R

According to question,

π(15)^2 – π(8)^2 = πR^2

⇒ 225π – 64π = πR^2

⇒ R^2 = 161

⇒ R = √161

Circumference of circle = 2πR

= 2π × √161

= 2√161 π cm