Question

A sphere of radius 7 cm with centre C and a larger sphere with centre E touches each other,
two common planks to both the spheres have an angle of 60° in between them. Then find
the radius of larger sphere.
0
21 cm
o
35 cm
c
V3 cm​

Answer 1

Given : A sphere of radius 7 cm with centre C and a larger sphere with centre E touches each other, two common planks to both the spheres have an angle of 60° in between them.

To find :  the radius of larger sphere.​

Solution:

Angle  between planks ( tangents) = 60°

Half of angle = 60/2 = 30°

Let Say Distance  of Common plank point = d

Sin 30°  =   7/( 7 + d)

=> 1/2 = 7/(7 + d)

=> 7 + d = 14

=> d = 7

Distance of center of sphere from common plank point

= d + 2 * 7  + r    ( r = radius of larger sphere)

= 7 + 14 + r

= 21 + r

Sin 30   =  r /(21 + r)

=> 1/2 = r/(21 + r)

=> 21 + r  =  2r

=> r = 21

Radius of larger sphere = 21 cm

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