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Question
Find the locus of the centre of a circle of radius r touching externally a circle of radius R.
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Solution
Let a circle of radius r (with centre B) touch a circle of radius R at C. Then ACB is a straight line and
AB = AC + CB = R + r
Thus, B moves such that its distance from fixed point. A remains constant and is equal to R + r.
Hence, the locus of B is a circle whose centre is A and radius equal to R + r.
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