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 = XY2
(r + 9)2 + (r + 2)2 = 289
r = 6 (r cannot be negative)