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Category: Mensuration

Question-185705

Question Number 185705 by Mingma last updated on 26/Jan/23 Answered by mr W last updated on 26/Jan/23 $${s}=\frac{{n}−\mathrm{1}+{n}+{n}+\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{3}{n}}{\mathrm{2}} \\ $$$$\overset{\_} {{r}}=\frac{{rs}}{{s}−{n}}=\frac{{r}}{\mathrm{1}−\frac{{n}}{{s}}}=\frac{{r}}{\mathrm{1}−\frac{\mathrm{2}{n}}{\mathrm{3}{n}}}=\mathrm{3}{r} \\ $$$$\frac{{r}}{\overset{\_} {{r}}}=\frac{\mathrm{1}}{\mathrm{3}}\:\checkmark \\…

Question-185372

Question Number 185372 by Mingma last updated on 20/Jan/23 Answered by a.lgnaoui last updated on 21/Jan/23 $$\bigtriangleup\mathrm{ODO}\:\:\:\mathrm{Triangle}\:\mathrm{rectangle} \\ $$$$\mathrm{O}_{\mathrm{1}} \mathrm{O}_{\mathrm{2}} ^{\mathrm{2}} =\left(\mathrm{O}_{\mathrm{1}} \mathrm{C}+\mathrm{CD}\right)^{\mathrm{2}} +\mathrm{O}_{\mathrm{2}} \mathrm{D}^{\mathrm{2}}…

Question-185166

Question Number 185166 by Rupesh123 last updated on 17/Jan/23 Answered by mnjuly1970 last updated on 18/Jan/23 $$\:\: \\ $$$${sin}\left(\frac{{A}}{\mathrm{2}}\:\right)\:=\:\frac{{r}}{{IA}}\:\Rightarrow\:{r}\:=\:{IA}.{sin}\left(\frac{{A}}{\mathrm{2}}\right) \\ $$$$\:\:\:\:\:\:{sin}\left(\:\frac{{B}}{\mathrm{2}}\right)=\:\frac{{r}}{{IB}}\:\Rightarrow\:{r}\:=\:{IB}.{sin}\left(\frac{{B}}{\mathrm{2}}\right) \\ $$$$\:\:\:\:\:\:{sin}\left(\frac{{C}}{\mathrm{2}}\right)=\frac{{r}}{{IC}}\:\Rightarrow\:{r}=\:{IC}.{sin}\left(\frac{{C}}{\:\mathrm{2}}\:\right) \\ $$$$\:\:\:\:−−−−−−−−−…