Category: Geometry

Question Number 174763 by dragan91 last updated on 10/Aug/22 Answered by a.lgnaoui last updated on 11/Aug/22 $$\angle{ADF} \\ $$$$\frac{\mathrm{sin}\:\mathrm{A}}{\mathrm{DF}}=\frac{\mathrm{sin}\:\mathrm{F}}{\mathrm{AD}}=\frac{\mathrm{sin}\:\mathrm{D}}{\mathrm{24}}\:\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\angle{EBF} \\ $$$$\frac{\mathrm{sin}\:\mathrm{B}}{\mathrm{x}}=\frac{\mathrm{sin}\:\mathrm{F}}{\mathrm{3}}=\frac{\mathrm{sin}\:\mathrm{E}}{\mathrm{8}}\:\:\:\:\:\:\:\left(\mathrm{2}\right) \\ $$$$\angle{CDE}…

Question Number 43621 by ajfour last updated on 12/Sep/18 Commented by math1967 last updated on 13/Sep/18 $${AD}=\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}\:\:\:,{AC}=\sqrt{{x}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{1}}=\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\bigtriangleup{ABD}\sim\bigtriangleup{CED}\:\therefore\frac{{ED}}{{x}}=\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}} \\…

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Question Number 43461 by MJS last updated on 10/Sep/18 $$\mathrm{found}\:\mathrm{something}\:\left(\mathrm{others}\:\mathrm{have}\:\mathrm{found}\:\mathrm{before}\right) \\ $$$$\mathrm{which}\:\mathrm{I}\:\mathrm{thought}\:\mathrm{might}\:\mathrm{be}\:\mathrm{of}\:\mathrm{interest}, \\ $$$$\mathrm{especially}\:\mathrm{for}\:\mathrm{Sir}\:\mathrm{Tanmay}\:\mathrm{Chaudhury}: \\ $$$$\mathrm{take}\:\mathrm{any}\:\mathrm{polynome}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{4}\:\mathrm{with}\:\mathrm{2}\:\mathrm{real} \\ $$$$\mathrm{inflection}\:\mathrm{points} \\ $$$${y}={ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e} \\ $$$${y}''=\mathrm{12}{ax}^{\mathrm{2}}…

Question Number 43360 by ajfour last updated on 10/Sep/18 Commented by ajfour last updated on 10/Sep/18 $${Find}\:\boldsymbol{{R}}\:{in}\:{terms}\:{of}\:\boldsymbol{{a}},\boldsymbol{{b}},\boldsymbol{{c}}. \\ $$ Commented by ajfour last updated on…