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Question-79694




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 α, β, γ 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.  (α+β≤c, β+γ≤a, γ+α≤b)
$${Three}\:{circles}\:{with}\:{radii}\:\alpha,\:\beta,\:\gamma\:{have} \\ $$$${their}\:{centres}\:{at}\:{the}\:{vertexes}\:{of}\:{a} \\ $$$${triangle}\:{with}\:{sides}\:{a},\:{b},\:{c}. \\ $$$${Find}\:{the}\:{radius}\:{R}\:{of}\:{the}\:{circle}\:{which} \\ $$$${touches}\:{the}\:{three}\:{circles}\:{from}\:{outside} \\ $$$${and}\:{the}\:{radius}\:{r}\:{of}\:{the}\:{circle}\:{which} \\ $$$${touches}\:{the}\:{three}\:{circles}\:{from}\:{inside}. \\ $$$$\left(\alpha+\beta\leqslant{c},\:\beta+\gamma\leqslant{a},\:\gamma+\alpha\leqslant{b}\right) \\ $$

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