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# Circles and Circles

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)]

(Google Images)

Note by Raymond Park
2 months, 2 weeks ago

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Use descartes' circle theorem. · 2 months, 2 weeks ago

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Any other way? · 2 months, 2 weeks ago

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Here's another way.

We first prove the following lemma:

Using this lemma, we get the following proof:

· 2 months, 2 weeks ago

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

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Well done! · 2 months, 1 week ago

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