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

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

## Comments

Sort by:

TopNewestSearch for descartes theorem. – Krishna Sharma · 2 years, 4 months ago

Log in to reply