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Question Number 84304 by Wepa last updated on 11/Mar/20

$$\mathrm{\Delta }\mathrm{ABC}\mathrm{AB}=\mathrm{a}\mathrm{BC}=\mathrm{b}\mathrm{AC}=\mathrm{c}$$$$\mathrm{and}\mathrm{\angle }\mathrm{C}=90°$$$$\mathrm{r}=?$$

Commented by mr W last updated on 11/Mar/20

$$r=\frac{ab}{a+b+c}$$

Answered by $@ty@m123 last updated on 11/Mar/20

$$Generalformula:$$$$r=\frac{△}{s},△=\frac{1}{2}ab\sin C$$$$HereC={90}^{\mathrm{o}}$$$$\therefore r=\frac{ab\sin {90}^{\mathrm{o}}}{2\times \frac{a+b+c}{2}}$$$$\Rightarrow r=\frac{ab}{a+b+c}$$

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