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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## Comments

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TopNewestUse descartes' circle theorem.

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Any other way?

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Here's another way.

We first prove the following lemma:

Using this lemma, we get the following proof:

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@Raymond Park Was this helpful?

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