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The centres of two circles C1 and C2 eac...

The centres of two circles C1 and `C2` each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1` and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is

Text Solution

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in `/_ PDO`
`/_PRO = 90^@`angle between tangent
let `/_ POR = alpha`
`/_APD = alpha = /_EPB` (V.O.A)
In `/_ PEB`
`BE=1` (radius)
`BP= 3`
`PE^2 = BD^2 - BE^2`
...
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