Question

X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centreb of a circle of radius 4 cm, which touches the above circles externally. Given that <XZY=90o, write an equation in r and solve it for r.

Answer 1

Let r be the radius of the third circle
XY = 17cm ⇒ XZ = 9 + r YZ = 2

APQ
(r + 9)² + (r + 2)² = (1 + r)²
  ⇒ r² + 18r + 81 + r² + 4r + 4 = 289S
 ⇒  r² + 11r - 10r = 0
(r + 17) (r – 6) = 0
 ⇒  r = - 17 (N.P)
r = 6 cm
Therefore, radius = 6cm.