# 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
3 years, 7 months ago

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