the distance between the centres of two circles whose radii 6 cm and 9 cm is 17 cm. another circle with centre O is touching both of these circles externally.find its radius

Answer :
we form our diagram from given information , As :

Here Radius of two circle 6  cm and 9 cm , and distance between their centers  =  17  cm

So,

Diameter of circle that touches given two circle externally  =  Distance between center of two circle  +  Radius of both circle
So,
AB  =  6   + 1 7 + 9  = 32 cm
So,
Radius OA  =  OB  =  16  cm                                        ( Ans )