Category: Geometry

Question Number 191455 by Mingma last updated on 24/Apr/23 Answered by a.lgnaoui last updated on 25/Apr/23 $$\:\bigtriangleup\mathrm{ANB}\:\:\:\mathrm{BM}\bot\mathrm{AN}\:\:\mathrm{et}\:\measuredangle\mathrm{MBA}=\measuredangle\mathrm{MBN} \\ $$$$\:\Rightarrow\mathrm{AB}=\mathrm{BN}=\frac{\boldsymbol{\mathrm{x}}}{\mathrm{cos}\:\boldsymbol{\theta}}\:\:\:\:\:\:\:\:\left(\mathrm{1}\right) \\ $$$$\:\bigtriangleup\mathrm{PNC}\:\:\:\:\:\:\mathrm{PC}=\mathrm{3cm} \\ $$$$\:\mathrm{BM}\mid\mid\:\mathrm{NP}\:\:\Rightarrow\:\measuredangle\:\mathrm{PNC}=\measuredangle\mathrm{MBN}=\theta=\measuredangle\mathrm{PCN} \\ $$$$\:\Rightarrow\mathrm{NP}=\mathrm{PC}=\mathrm{3}…

Question Number 191405 by Mingma last updated on 23/Apr/23 Commented by mr W last updated on 23/Apr/23 $${r}=\frac{{ab}}{\:\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }+\left(\mathrm{1}+\sqrt{\mathrm{3}}\right){a}+\mathrm{2}{b}} \\ $$$${with}\:{a}=\mathrm{3},\:{b}=\mathrm{4}: \\ $$$${r}=\frac{\mathrm{12}}{\:\mathrm{16}+\mathrm{3}\sqrt{\mathrm{3}}}\approx\mathrm{0}.\mathrm{566} \\…

Question Number 191403 by Mingma last updated on 23/Apr/23 Answered by mr W last updated on 23/Apr/23 $${as}\:{Q}\mathrm{191305}\:{but}\:\theta=\mathrm{45}° \\ $$$${r}=\frac{{ab}}{{a}+{b}+\sqrt{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }+\left({a}+\sqrt{\mathrm{3}}{b}\right)\mathrm{sin}\:\theta+\left(\sqrt{\mathrm{3}}{a}+{b}\right)\mathrm{cos}\:\theta} \\ $$$${with}\:\theta=\mathrm{45}° \\…

Question Number 60313 by ajfour last updated on 19/May/19 Commented by ajfour last updated on 19/May/19 $$\mathrm{Find}\:\mathrm{side}\:\mathrm{length}\:\boldsymbol{{l}}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:\mathrm{circumscribing}\:\mathrm{a}\:\mathrm{given} \\ $$$$\bigtriangleup\mathrm{ABC}\:\left(\mathrm{sides}\:\mathrm{a},\mathrm{b},\mathrm{c}\right). \\ $$ Answered by…

Question Number 125800 by TITA last updated on 13/Dec/20 Commented by TITA last updated on 13/Dec/20 $$\mathrm{prove} \\ $$ Commented by liberty last updated on…