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Category: Geometry

ABCD-is-a-square-with-side-length-1-E-is-a-moving-point-between-B-amp-C-F-is-a-moving-point-between-C-amp-D-Find-the-maximum-radius-of-inscribed-circle-in-AEF-

Question Number 90456 by Tony Lin last updated on 23/Apr/20 $${ABCD}\:{is}\:{a}\:{square}\:{with}\:{side}\:{length}=\mathrm{1} \\ $$$${E}\:{is}\:{a}\:{moving}\:{point}\:{between}\:{B\&C} \\ $$$${F}\:{is}\:{a}\:{moving}\:{point}\:{between}\:{C\&D} \\ $$$${Find}\:{the}\:{maximum}\:{radius}\:{of}\:{inscribed} \\ $$$${circle}\:{in}\:\bigtriangleup{AEF} \\ $$ Answered by mr W…

Question-90347

Question Number 90347 by mr W last updated on 22/Apr/20 Commented by mr W last updated on 22/Apr/20 $${the}\:{parabola}\:{has}\:{the}\:{same}\:{shape}\:{as} \\ $$$${y}={x}^{\mathrm{2}} .\:{find}\:{it}'{s}\:{equation}\:{if}\:{it}\:{passes} \\ $$$${through}\:{O},\:{A},\:{B}\:{as}\:{shown}. \\…

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}}…