Let Circle A be external tangent to Circle B. Let Circle C be external tangent to both Circle A and B. All three circles are external tangent to a line. Prove that for any given radius of Circle A and B, for example, x and y, respectively, the radius of the Circle C with radius z can be expressed as [1/sqrt(x)]+[1/sqrt(y)]= [1/sqrt(z)]

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TopNewestUse descartes' circle theorem. – Deeparaj Bhat · 2 months, 2 weeks ago

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– Raymond Park · 2 months, 2 weeks ago

Any other way?Log in to reply

We first prove the following lemma:

Using this lemma, we get the following proof:

– Deeparaj Bhat · 2 months, 2 weeks agoLog in to reply

@Raymond Park Was this helpful? – Deeparaj Bhat · 2 months, 2 weeks ago

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– Raymond Park · 2 months, 1 week ago

Well done!Log in to reply