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Category: Geometry

Question-185424

Question Number 185424 by ajfour last updated on 21/Jan/23 Commented by Frix last updated on 21/Jan/23 $$\mathrm{Impossible}. \\ $$$$\mathrm{tan}\:\theta\:=\frac{\left(\mathrm{2}\left({x}−\mathrm{1}\right)+\sqrt{{x}+\mathrm{2}}\right)\sqrt{{x}}}{\mathrm{4}{x}−\mathrm{1}} \\ $$ Commented by MJS_new last…

Question-54312

Question Number 54312 by ajfour last updated on 02/Feb/19 Commented by ajfour last updated on 02/Feb/19 Commented by ajfour last updated on 02/Feb/19 $${Given}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}\:;\:\:{find}\:\boldsymbol{{R}},\boldsymbol{{r}},\boldsymbol{{d}}. \\…

Question-185324

Question Number 185324 by cherokeesay last updated on 20/Jan/23 Answered by som(math1967) last updated on 20/Jan/23 $${AC}=\sqrt{\mathrm{2}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }=\sqrt{\mathrm{5}}={BC} \\ $$$$\:{r}×\frac{\mathrm{2}+\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{2}×\mathrm{1} \\ $$$$\Rightarrow{r}=\frac{\mathrm{2}}{\mathrm{3}+\sqrt{\mathrm{5}}} \\ $$$$\:{R}×\frac{\sqrt{\mathrm{5}}+\sqrt{\mathrm{5}}+\mathrm{2}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{2}×\mathrm{2}…