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Category: Geometry

Show-that-the-shortest-distance-between-two-opposite-edges-a-d-of-a-tetrahedron-is-6V-adsin-where-is-the-angle-between-the-edges-and-V-is-the-volume-of-the-tetrahedron-

Question Number 24778 by ajfour last updated on 25/Nov/17 $${Show}\:{that}\:{the}\:{shortest}\:{distance} \\ $$$${between}\:{two}\:{opposite}\:{edges}\:\boldsymbol{{a}},\boldsymbol{{d}}\: \\ $$$${of}\:{a}\:{tetrahedron}\:{is}\:\mathrm{6}\boldsymbol{{V}}/\boldsymbol{{ad}}\mathrm{sin}\:\boldsymbol{\theta}, \\ $$$${where}\:\theta\:{is}\:{the}\:{angle}\:{between}\:{the} \\ $$$${edges}\:{and}\:{V}\:{is}\:{the}\:{volume}\:{of}\:{the} \\ $$$${tetrahedron}. \\ $$ Commented by ajfour…

Question-90272

Question Number 90272 by student work last updated on 22/Apr/20 Answered by behi83417@gmail.com last updated on 22/Apr/20 $$\mathrm{AO}+\mathrm{OC}=\mathrm{8} \\ $$$$\mathrm{AO}^{\mathrm{2}} +\mathrm{OC}^{\mathrm{2}} =\mathrm{6}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{AO}.\mathrm{OC}=\frac{\mathrm{1}}{\mathrm{2}}\left[\left(\mathrm{AO}+\mathrm{OC}\right)^{\mathrm{2}} −\left(\mathrm{AO}^{\mathrm{2}}…

Let-ABCD-be-a-square-and-M-N-points-on-sides-AB-BC-respectably-such-that-MDN-45-If-R-is-the-midpoint-of-MN-show-that-RP-RQ-where-P-Q-are-the-points-of-intersection-of-AC-with-the-lines-MD-

Question Number 24684 by Tinkutara last updated on 24/Nov/17 $$\mathrm{Let}\:{ABCD}\:\mathrm{be}\:\mathrm{a}\:\mathrm{square}\:\mathrm{and}\:{M},\:{N}\:\mathrm{points} \\ $$$$\mathrm{on}\:\mathrm{sides}\:{AB},\:{BC}\:\mathrm{respectably},\:\mathrm{such}\:\mathrm{that} \\ $$$$\angle{MDN}\:=\:\mathrm{45}°.\:\mathrm{If}\:{R}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of} \\ $$$${MN}\:\mathrm{show}\:\mathrm{that}\:{RP}\:=\:{RQ}\:\mathrm{where}\:{P},\:{Q} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{points}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{of}\:{AC}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{lines}\:{MD},\:{ND}. \\ $$ Terms of Service…

Question-155701

Question Number 155701 by ajfour last updated on 03/Oct/21 Commented by ajfour last updated on 03/Oct/21 $${If}\:{the}\:{blue}\:{triangle}\:{is}\:{equilateral} \\ $$$${find}\:{the}\:{radius}\:{ratio}. \\ $$$$\left({the}\:{center}\:{of}\:{both}\:{circles}\:{lie}\:{on}\:{the}\right. \\ $$$$\left.\:\:\:{same}\:{vertical}\right) \\ $$…

Question-90161

Question Number 90161 by I want to learn more last updated on 21/Apr/20 Answered by me2love2math last updated on 21/Apr/20 $${the}\:{square}\:{has}\:{a}\:{larger}\:{perimeter}…. \\ $$$${draw}\:\boldsymbol{{a}}\:\boldsymbol{{chord}}\:\boldsymbol{{that}}\:\boldsymbol{{run}}\:\boldsymbol{{through}}\:\boldsymbol{{the}}\:\boldsymbol{{centre}}\:\boldsymbol{{o}} \\ $$$$\boldsymbol{{centre}}\:\boldsymbol{{of}}\:\boldsymbol{{circle}}\:\boldsymbol{{and}}\:\boldsymbol{{apply}}\:\boldsymbol{{law}}\:\boldsymbol{{of}}\:…