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Inradius

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The inradius of a polygon is the radius of its incircle (assuming an incircle exists). It is commonly denoted $r$ .

Properties

If $\triangle ABC$ has inradius $r$ and circumradius $R$ , then $\cos{A}+\cos{B}+\cos{C}=\frac{r+R}{R}$ .
If $\triangle ABC$ has inradius $r$ and semi-perimeter $s$ , then the area of $ABC$ is $rs$ .

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Geometry

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