﻿ A circle C1 of radius b touches the circle x2 + y2 = a2 externally and has its centre on the positive x-axis; another circle C2 of radius c touches the circle C1 externally and has its centre on the positive x-axis. Given a< b < c, then the three circles have a common tangent if a, b, c are in  : Kaysons Education

# A Circle C1 of Radius b touches The Circle x2 + y2 = a2 externally And Has Its Centre On The Positive x-axis; Another Circle C2 of Radius c touches The Circle C1 externally And Has Its Centre On The Positive x-axis. Given a< b < c, Then The Three Circles Have A Common Tangent If a, b, c are In

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## Question

### Solution

Correct option is

G.P.

The centre of C1 is (a + b, 0) and the centre of C2 is

(a + 2b + c, 0)

Let y = mx + k be a tangent common to the three circles.

Since it touches x2 + y2 = a2C1 and C2

As the centre of the three circles lie on the same side of the line y = mxk, taking the same sign, say positive, in the three relations we get,

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