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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=90o, 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
⇒ r2 + 18r + 81 + r2 + 4r + 4 = 289S
⇒ r2 + 11r - 10r = 0 (r + 17) (r - 6) = 0
⇒ r = - 17 (N.P)
r = 6 cm
∴radius = 6cm
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