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Category: Geometry

if-the-on-ABC-inner-circle-radius-and-outer-circle-radius-r-and-R-show-that-r-4R-sin-A-2-sin-B-2-sin-C-2-

Question Number 188320 by normans last updated on 27/Feb/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{on}}\:\bigtriangleup\boldsymbol{{ABC}},\: \\ $$$$\:\:\boldsymbol{{inner}}\:\boldsymbol{{circle}}\:\boldsymbol{{radius}}\:\boldsymbol{{and}}\:\boldsymbol{{outer}}\:\boldsymbol{{circle}}\:\boldsymbol{{radius}}\:\boldsymbol{{r}}\:\boldsymbol{{and}}\:\boldsymbol{{R}}\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\boldsymbol{{show}}\:\boldsymbol{{that}}; \\ $$$$\:\:\:\:\:\:\boldsymbol{{r}}\:=\:\mathrm{4}\boldsymbol{{R}}\:\boldsymbol{{sin}}\:\frac{\boldsymbol{{A}}}{\mathrm{2}}\:\centerdot\:\boldsymbol{{sin}}\:\frac{\boldsymbol{{B}}}{\mathrm{2}}\:\centerdot\:\boldsymbol{{sin}}\:\frac{\boldsymbol{{C}}}{\mathrm{2}} \\ $$$$ \\ $$ Answered by mr…

Question-188296

Question Number 188296 by Rupesh123 last updated on 27/Feb/23 Answered by HeferH last updated on 27/Feb/23 $$\mathrm{2}^{\mathrm{2}} \:=\:\mathrm{1}\centerdot{h}\:\Rightarrow\:{h}\:=\:\mathrm{4}\: \\ $$$$\:{h}^{\mathrm{2}} \:=\:\mathrm{2}{x} \\ $$$$\:\mathrm{16}\:=\:\mathrm{2}{x} \\ $$$$\:{x}\:=\:\mathrm{8}\:…

Question-57186

Question Number 57186 by Tawa1 last updated on 31/Mar/19 Commented by kaivan.ahmadi last updated on 31/Mar/19 $$\begin{vmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{{a}\:\:\:\:\:\:\:\:\:\:{b}\:\:\:\:\:\:\:\:\:\:\:{c}}\\{{a}^{\mathrm{2}} \:\:\:\:\:\:\:\:{b}^{\mathrm{2}} \:\:\:\:\:\:{c}^{\mathrm{2}} }\end{vmatrix}\underset{−{a}^{\mathrm{2}} {R}_{\mathrm{1}} +{R}_{\mathrm{3}} } {\overset{−{aR}_{\mathrm{1}} +{R}_{\mathrm{2}}…