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Category: Geometry

answer-to-the-question-number-197017-AF-FI-amp-AG-GJ-FG-1-2-IJ-1-6-BC-FGH-is-squilatral-FGH-ABC-S-FGH-S-SBC-1-36-

Question Number 197287 by MM42 last updated on 13/Sep/23 $${answer}\:{to}\:{the}\:{question}\:{number} \\ $$$$\mathrm{197017} \\ $$$${AF}={FI}\:\&\:\:{AG}={GJ}\Rightarrow{FG}=\frac{\mathrm{1}}{\mathrm{2}}{IJ}=\frac{\mathrm{1}}{\mathrm{6}}{BC} \\ $$$$\bigtriangleup{FGH}\:\:{is}\:\:{squilatral}\:\Rightarrow\:\bigtriangleup{FGH}\approx\bigtriangleup{ABC} \\ $$$$\Rightarrow\frac{{S}_{{FGH}} }{{S}_{{SBC}} }\:=\frac{\mathrm{1}}{\mathrm{36}\:}\:\checkmark \\ $$$$ \\ $$ Commented…

Question-197095

Question Number 197095 by Mingma last updated on 07/Sep/23 Answered by mahdipoor last updated on 07/Sep/23 $$\frac{{AB}}{{sin}\mathrm{4}{a}}=\frac{{BM}}{{sina}}\:\:\: \\ $$$$\:\frac{{CD}}{{sin}\mathrm{4}{a}}=\frac{{MC}}{{sin}\mathrm{2}{a}}\Rightarrow\frac{\mathrm{2}.{CD}.{cosa}}{{sin}\mathrm{4}{a}}=\frac{{MC}}{{sina}}\Rightarrow \\ $$$$\frac{{MC}}{{sina}}+\frac{{BM}}{{sina}}=\frac{{CB}}{{sina}}=\frac{\mathrm{2}.{CD}.{cosa}}{{sin}\mathrm{4}{a}}+\frac{{AB}}{{sin}\mathrm{4}{a}} \\ $$$$\Rightarrow\frac{{sin}\mathrm{4}{a}}{{sina}}=\mathrm{4}{cos}\mathrm{2}{a}.{cosa}=\mathrm{2}{cosa}+\mathrm{1}\Rightarrow \\ $$$$\mathrm{8}{cos}^{\mathrm{3}}…

Question-196829

Question Number 196829 by cortano12 last updated on 01/Sep/23 Answered by universe last updated on 01/Sep/23 $${by}\:{apollonius}\:{theorem} \\ $$$${BC}^{\mathrm{2}} \:+\:{PC}^{\mathrm{2}\:} \:=\:\mathrm{2}\left({QC}^{\mathrm{2}} +{PQ}^{\mathrm{2}} \right)\:\:\:…..\left(\mathrm{1}\right) \\ $$$${AC}^{\mathrm{2}}…

prove-that-the-curve-x-1-2-y-2-x-1-2-y-2-4-is-an-ellipse-and-find-its-semi-major-axis-and-semi-minor-axis-

Question Number 196723 by mr W last updated on 30/Aug/23 $${prove}\:{that}\:{the}\:{curve}\: \\ $$$$\sqrt{\left({x}−\mathrm{1}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} }+\sqrt{\left({x}+\mathrm{1}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} }=\mathrm{4}\: \\ $$$${is}\:{an}\:{ellipse}\:{and}\:{find}\:{its}\:{semi} \\ $$$${major}\:{axis}\:{and}\:{semi}\:{minor}\:{axis}. \\ $$ Answered by…

Question-196275

Question Number 196275 by AROUNAMoussa last updated on 21/Aug/23 Answered by MM42 last updated on 21/Aug/23 $$\langle{ABD}=\mathrm{35}\Rightarrow{AD}={AB} \\ $$$$\langle{BCD}=\mathrm{55} \\ $$$$\frac{{AB}}{{AC}}=\frac{{sinx}}{{sin}\mathrm{130}}\:\:\:\&\:\:\frac{{AD}}{{AC}}=\frac{{sin}\left(\mathrm{55}−{x}\right)}{{sin}\mathrm{65}} \\ $$$$\Rightarrow{sinx}×{sin}\mathrm{65}=\mathrm{2}{sin}\mathrm{65}×{cos}\mathrm{65}×{sin}\left(\mathrm{55}−{x}\right) \\ $$$$\Rightarrow{sinx}=\mathrm{2}{cos}\mathrm{65}{sin}\left(\mathrm{55}−{x}\right)={sin}\left(\mathrm{55}−{x}+\mathrm{65}\right)+{sin}\left(\mathrm{55}−{x}−\mathrm{65}\right)…