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Category: Geometry

Question-201322

Question Number 201322 by cherokeesay last updated on 04/Dec/23 Answered by AST last updated on 05/Dec/23 $${Let}\:\angle{EDC}=\beta\Rightarrow\angle{ABD}=\mathrm{2}\beta−\mathrm{90} \\ $$$${EC}^{\mathrm{2}} =\mathrm{2}−\mathrm{2}{cos}\beta…\left({i}\right) \\ $$$${BC}^{\mathrm{2}} ={BD}^{\mathrm{2}} +\mathrm{1}−\mathrm{2}{BD}\boldsymbol{{D}}{Ccos}\left(\mathrm{2}\beta\right)…\left({ii}\right) \\…

Question-201150

Question Number 201150 by Mingma last updated on 30/Nov/23 Answered by mr W last updated on 02/Dec/23 $${a}={side}\:{length}\:{of}\:{square} \\ $$$$\left(\frac{{a}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{15}^{\mathrm{2}} }{\mathrm{2}{ax}}\right)^{\mathrm{2}} +\left(\frac{{a}^{\mathrm{2}} +{x}^{\mathrm{2}}…

Question-201037

Question Number 201037 by mr W last updated on 28/Nov/23 Commented by mr W last updated on 28/Nov/23 $${a}\:{triangle}\:{has}\:{sides}\:{a},\:{b},\:{c}.\:{find}\:{the} \\ $$$${fraction}\:{of}\:{its}\:{area}\:{covered}\:{by}\:{all} \\ $$$$\left({infinite}\right)\:{inscribed}\:{circles}\:{as}\:{shown}. \\ $$…