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

XZ^{2 }+ ZY^{2} = XY^{2 }

(*r* + 9)^{2 }+ (*r* + 2)^{2 }= 289

*r *= 6 (*r* cannot be negative)* *

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