Question

As shown in the figure, the five circles are tangent to one another consecutively and to the lines L₁ and L₂. If the radius of the largest circle is 18 and that of the smaller one is 8, then find the radius of the middle circle.

Answer 1

 Radius of largest circle = 18 

Radius of smallest circle = 8

When 3 circle touching each other have direct common tangent 

The radius of the middle circle is GM of radius of other 2 circles

∴ r²₂ = r₁ r₃

In the given problem 

Let radius of middle circle be r,

2^nd smallest circle be r₁ & 2nd largest circle be r₂