X &Y are centres of circles of radius 9cm, 2cm and XY=17cm.Z is the centre ofcircle of radius r cm, which touches the above circle externally given that XZY=90degree. Write an equation inr and solve it for r

Let the radius of the circle touching the two circle with centres X and Y be r cm. 

If two circles touch each other externally, then sum of their radii is equal to the distance between their centres.

XZ = r + 9

ZY = r +2

XY = 17

Given, ∠XZY = 90º

XZ2 + ZY2 = XY

(r + 9)2 + (r + 2)= 289

r = 6  (r cannot be negative) 

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