Question Number 79694 by mr W last updated on 27/Jan/20
Commented by mr W last updated on 27/Jan/20
$${Three}\:{circles}\:{with}\:{radii}\:\alpha,\:\beta,\:\gamma\:{have} \\ $$$${their}\:{centres}\:{at}\:{the}\:{vertexes}\:{of}\:{a} \\ $$$${triangle}\:{with}\:{sides}\:{a},\:{b},\:{c}. \\ $$$${Find}\:{the}\:{radius}\:{R}\:{of}\:{the}\:{circle}\:{which} \\ $$$${touches}\:{the}\:{three}\:{circles}\:{from}\:{outside} \\ $$$${and}\:{the}\:{radius}\:{r}\:{of}\:{the}\:{circle}\:{which} \\ $$$${touches}\:{the}\:{three}\:{circles}\:{from}\:{inside}. \\ $$$$\left(\alpha+\beta\leqslant{c},\:\beta+\gamma\leqslant{a},\:\gamma+\alpha\leqslant{b}\right) \\ $$