JEE Advanced 2009 Mathematics question
The centres of two circles and 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 and and C be a circle touching circles and externally. If a common tangent to and C passing through P is also a common tangent to and C, then the radius of the circle C is
Answer: 8
Solution
By symmetry the centre of C lies on the perpendicular bisector of , at distance h from P; let its radius be r. External contact: . The common tangent through P touches and C, so
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