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Category: Geometry

Question-67254

Question Number 67254 by TawaTawa last updated on 24/Aug/19 Commented by Rasheed.Sindhi last updated on 24/Aug/19 $$\:\:\:\:\:{Analytical}\:{Method} \\ $$$${x}-{axis}:{Horizanal}\:{Chord} \\ $$$${y}-{axis}:{Vertical}\:{Chord} \\ $$$${Three}\:{points}\:{on}\:{the}\:{circle}: \\ $$$$\:{A}\left(\mathrm{6},\mathrm{0}\right),{B}\left(−\mathrm{2},\mathrm{0}\right)\:\&\:{C}\left(\mathrm{0},−\mathrm{3}\right)…

A-right-angled-triangle-has-fixed-hypotenuse-measuring-h-units-What-are-the-measures-of-its-legs-for-maximum-perimeter-P-units-Will-the-area-be-also-maximum-when-the-perimeter-be-maximum-

Question Number 1611 by Rasheed Soomro last updated on 26/Aug/15 $$\mathrm{A}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle}\:\mathrm{has}\:\mathrm{fixed}\:\mathrm{hypotenuse}\:\mathrm{measuring} \\ $$$$\mathrm{h}\:\mathrm{units}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{measures}\:\:\mathrm{of}\:\mathrm{its}\:\mathrm{legs}, \\ $$$$\mathrm{for}\:\boldsymbol{\mathrm{maximum}}\:\boldsymbol{\mathrm{perimeter}}\:\mathrm{P}\:\mathrm{units}. \\ $$$$\mathrm{Will}\:\mathrm{the}\:\mathrm{area}\:\mathrm{be}\:\mathrm{also}\:\mathrm{maximum},\:\mathrm{when}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{be} \\ $$$$\mathrm{maximum}? \\ $$ Commented by Rasheed Soomro…

I-have-a-loop-of-string-of-length-perimeter-p-units-I-want-to-make-a-triangle-of-largest-area-from-the-loop-What-will-be-the-dimensions-of-that-triangle-

Question Number 1592 by Rasheed Soomro last updated on 23/Aug/15 $$\mathrm{I}\:\mathrm{have}\:\mathrm{a}\:\mathrm{loop}\:\mathrm{of}\:\mathrm{string}\:\mathrm{of}\:\mathrm{length}\left(\mathrm{perimeter}\right)\:\:\mathrm{p}\:\mathrm{units}.\: \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{make}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{area}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{loop}.\:\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{dimensions}\:\mathrm{of}\:\mathrm{that}\:\mathrm{triangle}? \\ $$ Commented by 123456 last updated on 23/Aug/15 $${x}+{y}+{z}={p}…

Find-a-function-f-x-satisfying-the-following-equation-a-b-1-2-f-x-2-f-x-2-d-dx-f-x-2-dx-0-b-gt-0-a-gt-0-b-a-

Question Number 1581 by 112358 last updated on 21/Aug/15 $${Find}\:{a}\:{function}\:{f}\left({x}\right)\:{satisfying} \\ $$$${the}\:{following}\:{equation}. \\ $$$$\int_{{a}} ^{\:{b}} \left[\frac{\mathrm{1}}{\mathrm{2}}\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} −\sqrt{\left\{{f}\left({x}\right)\right\}^{\mathrm{2}} +\left\{\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)\right\}^{\mathrm{2}} }\right]{dx}=\mathrm{0} \\ $$$${b}>\mathrm{0},{a}>\mathrm{0}\:,\:{b}\neq{a}.\:\: \\ $$ Commented by…

Question-67071

Question Number 67071 by TawaTawa last updated on 22/Aug/19 Commented by Prithwish sen last updated on 22/Aug/19 $$\left.\mathrm{a}\right)\mathrm{The}\:\mathrm{eqn}.\:\mathrm{of}\:\boldsymbol{\mathrm{C}}\:\:\left(\mathrm{x}−\mathrm{8}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \\ $$$$\because\:\boldsymbol{\mathrm{L}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tangent} \\ $$$$\therefore\:\frac{\mathrm{k}.\mathrm{8}−\mathrm{5}.\mathrm{2}−\mathrm{21}}{\:\sqrt{\mathrm{k}^{\mathrm{2}} +\mathrm{25}}}\:=\:\mathrm{r}…

Question-67033

Question Number 67033 by TawaTawa last updated on 22/Aug/19 Commented by Tony Lin last updated on 22/Aug/19 $${let}\angle{DBM}=\angle{MBC}=\phi \\ $$$$\:\:\:\:\:\angle{ECM}=\angle{MCB}=\theta \\ $$$$\mathrm{2}\theta+\mathrm{2}\phi=\mathrm{90}° \\ $$$$\Rightarrow\theta=\mathrm{45}°−\phi \\…