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The centres of two `C_1` and `C_2`, each unit of unit radii, are at a distance of 6 units from each other. Let P be the mid-point of the line segment joining the centres of `C_1 and C_2`. A third circle C is drawn such that it is externally tangent to both the circles `C_1 and C_2` at the same points where the lines passing through P are tangent to the circles `C_1 and C_2`. The radius of the circle C is

A

8

B

6

C

`6sqrt2`

D

`4sqrt2`

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The correct Answer is:
A
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