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The centres of two circles C1 and C2, ea...

The centres of two circles `C_1` and `C_2`, 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 `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.

Text Solution

Verified by Experts

`/_O'PQ=alpha=/_RPO`
(vartical opposite angle)
`/_CPR=90^0-alpha`
`O'Q=1`
`PO'=3`
PQ=`sqrt(PO'^2-O'Q^2`
PQ=`sqrt(9-1)=sqrt8=2sqrt2`
`/_PO'Q`
...
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