Category: Geometry

Question Number 184398 by HeferH last updated on 06/Jan/23 Answered by som(math1967) last updated on 06/Jan/23 $$\:\frac{{BD}}{{BC}}=\frac{{sin}\mathrm{2}\phi}{{sin}\left(\mathrm{180}−\mathrm{3}\phi\right)}=\frac{{sin}\mathrm{2}\phi}{{sin}\mathrm{3}\phi} \\ $$$$\frac{{AD}}{{BD}}=\frac{{sin}\mathrm{90}}{{sin}\left(\mathrm{90}−\mathrm{3}\phi\right)}=\frac{\mathrm{1}}{{cos}\mathrm{3}\phi} \\ $$$$\:{BD}={ADcos}\mathrm{3}\phi \\ $$$$\:\frac{{ADcos}\mathrm{3}\phi}{{AD}}=\frac{{sin}\mathrm{2}\phi}{{sin}\mathrm{3}\phi}\:\:\:\left[\because{BC}={AD}\right] \\ $$$${sin}\mathrm{3}\phi{cos}\mathrm{3}\phi={sin}\mathrm{2}\phi…

Question Number 184352 by cherokeesay last updated on 05/Jan/23 Answered by som(math1967) last updated on 05/Jan/23 $$\bigtriangleup{ABC}\sim\bigtriangleup{ACD} \\ $$$$\:\Rightarrow{x}^{\mathrm{2}} =\mathrm{6}×\mathrm{4}\Rightarrow{x}=\sqrt{\mathrm{24}}=\mathrm{2}\sqrt{\mathrm{6}} \\ $$$${BC}=\sqrt{\mathrm{4}×\mathrm{2}}=\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\bigtriangleup{AFE}\sim\bigtriangleup{ABC} \\…

Question Number 118811 by ajfour last updated on 19/Oct/20 Commented by ajfour last updated on 19/Oct/20 $${What}\:{is}\:{the}\:{side}\:{length}\:{of}\:{the}\:{equal} \\ $$$${sided}\:{hexagon}\:{inscribed}\:{within}\:{the} \\ $$$${triangle}\:{ABC}\:{as}\:{shown}? \\ $$ Commented by…

Question Number 53252 by ajfour last updated on 19/Jan/19 Commented by ajfour last updated on 19/Jan/19 $${Find}\:{a}\:{and}\:{r}\:{in}\:{terms}\:{of}\:{b}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…

Question Number 53168 by ajfour last updated on 18/Jan/19 Commented by ajfour last updated on 19/Jan/19 $${Equilateral}\:\bigtriangleup{ABC}\:\:{contains} \\ $$$${two}\:{circles}\:\:{of}\:{radii}\:{a}\:{and}\:{b}\:{in}\:{the} \\ $$$${manner}\:{shown}.\:{Find}\:{the}\:{radius} \\ $$$${R}\:{of}\:{a}\:{circle}\:{that}\:{touches}\:{these}\:{two} \\ $$$${circles}\:{externally}\:{and}\:{passes}\:{through}…