Category: Geometry

Question Number 207482 by cherokeesay last updated on 17/May/24 Answered by mr W last updated on 17/May/24 $${x}\left({a}−{x}\right)={yb}={zc} \\ $$$$\Rightarrow{y}=\frac{{x}\left({a}−{x}\right)}{{b}} \\ $$$$\Rightarrow{z}=\frac{{x}\left({a}−{x}\right)}{{c}} \\ $$$${d}^{\mathrm{2}} ={y}^{\mathrm{2}}…

Question Number 207426 by mr W last updated on 14/May/24 Answered by A5T last updated on 14/May/24 Commented by A5T last updated on 14/May/24 $${a}^{\mathrm{2}}…

Question Number 207362 by mr W last updated on 12/May/24 Answered by A5T last updated on 12/May/24 $${Ptolemy}'{s}\:{theorem}:\:{AC}×{BP}={AP}×{BC}+{AB}×{PC} \\ $$$${AB}={AC}={BC}\Rightarrow{PB}={PA}+{PC} \\ $$ Answered by sniper237…

Question Number 207230 by mr W last updated on 10/May/24 Answered by mr W last updated on 10/May/24 Commented by mr W last updated on…

Question Number 207035 by mr W last updated on 04/May/24 Answered by A5T last updated on 04/May/24 $${BE}=\sqrt{\mathrm{6}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }=\mathrm{2}\sqrt{\mathrm{10}}\Rightarrow{EF}={FB}=\sqrt{\mathrm{10}} \\ $$$${Let}\:{the}\:{line}\:{through}\:{F}\:{parallel}\:{to}\:{BC}\:{meet}\:{AB},{DC} \\ $$$${at}\:{H},{I}\:{resp}.,{then}\:{BH}=\mathrm{3}={DI};\:{FH}=\mathrm{1} \\…