X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally. Given that XZY=90^{o}, write an equation in r and solve it for r.
Ans: Let r be the radius of the third circle APQ
XY = 17cm ⇒ XZ = 9 + r YZ = 2
(r + 9)^{2} + (r + 2)^{2} = (1 + r)2
⇒ r^{2} + 18r + 81 + r^{2} + 4r + 4 = 289S
⇒ r^{2} + 11r - 10r = 0 (r + 17) (r - 6) = 0
⇒ r = - 17 (N.P)
r = 6 cm
∴radius = 6cm