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Category: Geometry

Question-37447

Question Number 37447 by ajfour last updated on 13/Jun/18 Commented by ajfour last updated on 13/Jun/18 $${Find}\:{the}\:{maximum}\:{elliptic}\:{area} \\ $$$$\left({in}\:{the}\:{shown}\:{orientation}\right)\: \\ $$$${cicumscribed}\:{by}\:{the}\:{isosceles} \\ $$$${triangle}. \\ $$…

Question-102836

Question Number 102836 by ajfour last updated on 11/Jul/20 Commented by ajfour last updated on 11/Jul/20 $$\bigtriangleup{ABC}\:{is}\:{equilateral}\:{with}\:{side}\:{a}. \\ $$$${If}\:{regions}\:\mathrm{1},\mathrm{2},\mathrm{3}\:{have}\:{equal} \\ $$$${perimeters},\:{find}\:{x}/{a}. \\ $$ Answered by…

Question-168347

Question Number 168347 by cortano1 last updated on 08/Apr/22 Commented by mr W last updated on 09/Apr/22 $${see}\:{Q}\mathrm{128303} \\ $$$${s}=\sqrt{\mathrm{3}}\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right)+\sqrt{\mathrm{3}\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} \right)^{\mathrm{2}} −\mathrm{8}{r}_{\mathrm{1}}…

Question-37209

Question Number 37209 by ajfour last updated on 10/Jun/18 Commented by ajfour last updated on 11/Jun/18 $${Find}\:{the}\:{circumradius}\:\boldsymbol{{R}}\:{of}\:{the} \\ $$$${three}\:{circles}\:\left({of}\:{radii}\:{a},{b},\:{c}\right)\:{in} \\ $$$${terms}\:{of}\:\boldsymbol{{a}},\boldsymbol{{b}}\:. \\ $$$${Also}\:{given}\:\boldsymbol{{c}}=\frac{\boldsymbol{{a}}+\boldsymbol{{b}}}{\mathrm{2}}\:. \\ $$…

Question-168206

Question Number 168206 by Tawa11 last updated on 06/Apr/22 Answered by MikeH last updated on 06/Apr/22 $${T}\mathrm{cos}\:\mathrm{30}\:=\:\mathrm{60}\:\Rightarrow\:{T}\:=\:\mathrm{60}×\frac{\mathrm{2}}{\:\sqrt{\mathrm{3}}}\:=\:\mathrm{40}\sqrt{\mathrm{3}}\:\mathrm{N} \\ $$ Commented by Tawa11 last updated on…