The centres of two circles `C_(1) and C_(2)` each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of `C_(1) and C_(2)` and C be a circle touching circles `C_(1) and C_(2)` externally. If a common tangent to `C_(1)` and C passing through P is also a common tangent to `C_(2)` and C, then the radius of the circle C, is

Answer

8

Explanation

P is mid point of AB and DP `_|_` AB.
In `Delta PFB cos alpha = (2sqrt(2))/(30`
`:. Sin alpha = (1)/(3)`
In `Delta DEP`
`tan alpha = (2sqrt(2))/(R )`
`R = (2 sqrt(2))/(tan alpha ) =` 8 units