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Inscribed circle in 3 arbitrary tangent circles. (help meh!)

3 circles \(A,B,C\) with radius \(a,b,c\) respectively, such that circles \(A,B,C\) are mutually tangent to each other. Let \(R\) be the circle that is internally tangent to circle \(A,B,C\), and \(R\) has a radius \(r\). Prove that

\[r = \frac{abc}{ab+bc+ca+2\sqrt{abc(a+b+c)}}\]

Note by Samuraiwarm Tsunayoshi
1 year, 11 months ago

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Search for descartes theorem. Krishna Sharma · 1 year, 11 months ago

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