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JEE Advanced2009MathematicsCircleActual

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 tangents to C₁ and C passing through P is also a common tangent to C₂ and C , then the radius of the circle C is

Correct answer

8

Step-by-step solution

(r+1)^2= ^2+9 array lc & r^2+8= ^2 & r^2+2 r+1=r^2+8+9 & 2 r=16 r=8 array

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