Write an equation in radius and solve it for radius, Mathematics

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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=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

⇒ 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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