Category: Geometry

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}…

Question Number 53071 by behi83417@gmail.com last updated on 16/Jan/19 Commented by behi83417@gmail.com last updated on 16/Jan/19 $${as}\:{shown}\:{in}\:{fig}: \\ $$$${prove}\:{that}: \\ $$$$\:\:\:\:\:\:\:\:\rightarrow\:\frac{\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{of}}\:\:{outer}\:\:\boldsymbol{\mathrm{hexagon}}}{\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{of}}\:\:{inner}\:\boldsymbol{\mathrm{triangle}}}\:\:\:\geqslant\:\mathrm{13} \\ $$ Commented by…