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Category: Geometry

If-a-circle-of-radius-r-is-inscribed-in-a-triangl-ABC-Express-r-in-terms-of-a-b-and-c-only-

Question Number 202001 by necx122 last updated on 18/Dec/23 $${If}\:{a}\:{circle}\:{of}\:{radius}\:{r}\:{is}\:{inscribed}\:{in} \\ $$$${a}\:{triangl}\:{ABC}.\:{Express}\:{r}\:{in}\:{terms}\:{of} \\ $$$${a},{b}\:{and}\:{c}\:{only} \\ $$ Answered by AST last updated on 18/Dec/23 $${r}=\frac{\sqrt{{s}\left({s}−{a}\right)\left({s}−{b}\right)\left({s}−{c}\right)}}{{s}}\:{where}\:{s}=\frac{{a}+{b}+{c}}{\mathrm{2}} \\…

Question-201907

Question Number 201907 by mnjuly1970 last updated on 15/Dec/23 Answered by Rasheed.Sindhi last updated on 15/Dec/23 $$\bullet{Radius}\:{of}\:{Semi}-{circle}\:{R}=\:\frac{\mathrm{10}}{\mathrm{2}}=\mathrm{5}\:{cm} \\ $$$$\bullet{let}\:{radous}\:{of}\:{greater}\:{quarter}-{circle}={r}_{\mathrm{1}} \\ $$$$\left({R}+{r}_{\mathrm{1}} \right)^{\mathrm{2}} =\mathrm{10}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} =\mathrm{125}…