JEE Advanced Mathematics question
The centres of two circles and each of unit radius are at a distance of 6 units from each other. Let be the mid-point of the line segment joining the centres of and , and be a circle touching circles and externally. If a common tangent to and passing through is also a common tangent to and then the radius of the circle is
Answer: 8
Solution
Take the centres , , so . Since touches both and externally, its centre is equidistant from and : centre , radius , with
DA = = 1 + r. (1)
A line through tangent to : with $ = 1 ⇒
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