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Category: Geometry

Question-45930

Question Number 45930 by Tawa1 last updated on 18/Oct/18 Answered by MJS last updated on 19/Oct/18 $$\mathrm{for}\:\mathrm{any}\:\mathrm{shape} \\ $$$$\mathrm{length}\:\left(\mathrm{or}\:\mathrm{radius},\:\mathrm{height},\:\mathrm{width}…\right)\:×{k} \\ $$$$\Rightarrow\:\mathrm{area}×{k}^{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{volume}\:×{k}^{\mathrm{3}} \\ $$$${l}×{k}\:\Rightarrow\:{a}×{k}^{\mathrm{2}}…

Determiner-la-hauteur-DE-r-x-en-fonction-de-r-r-OOC-BH-BF-20-pour-que-distance-AB-BC-CD-DE-EF-soit-sgale-AC-arcCDF-

Question Number 176913 by a.lgnaoui last updated on 28/Sep/22 $${Determiner}\:{la}\:{hauteur}\:\mathrm{D}{E}\left({r}+{x}\right)\:{en}\:{fonction}\:{de}\:{r} \\ $$$${r}=\mathrm{OOC}=\mathrm{BH}\:\:\:\:\:\mathrm{BF}=\mathrm{20} \\ $$$$\mathrm{pour}\:\mathrm{que}\:\mathrm{distance}\left(\mathrm{AB}+\mathrm{BC}+\mathrm{CD}+\mathrm{DE}+\mathrm{EF}\:\:\mathrm{soit}\:\right. \\ $$$$\mathrm{sgale}\:\mathrm{AC}+\mathrm{arcCDF} \\ $$ Commented by a.lgnaoui last updated on 28/Sep/22…

Question-45785

Question Number 45785 by Tawa1 last updated on 16/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 16/Oct/18 $${let}\:{centre}\:{of}\:{circle}\:{is}\:\left(\alpha,\beta\right)\:{and}\:{radius}\:{r} \\ $$$${so}\:{eqn}\:{of}\:{circle}\:\left({x}−\alpha\right)^{\mathrm{2}} +\left({y}−\beta\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${now}\:{as}\:{per}\:{condition} \\ $$$$\left.\mathrm{1}\right){x}\:{axis}\:{is}\left[{the}\:{tangent}\:{of}\:{circle}\:{so}\:{distance}\right.…

Question-45753

Question Number 45753 by Tawa1 last updated on 16/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 16/Oct/18 $${for}\:{cylnder}\:{volume}\:=\pi{R}^{\mathrm{2}} {H}\:\:{when}\:{base}\:{is}\:{circle} \\ $$$${of}\:{area}\:\pi{R}^{\mathrm{2}} \\ $$$${but}\:{here}\:{volume}\:{is}\:{sector}\:{aresfor}\:\mathrm{30}^{{o}} ×{height} \\ $$$${requiref}\:{volume}\:{is}…

Find-the-maximum-area-of-a-triangle-whose-vertices-lie-on-a-regular-hexagon-of-unit-area-

Question Number 111284 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{whose}\:\mathrm{vertices}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{a}\:\mathrm{regular} \\ $$$$\mathrm{hexagon}\:\mathrm{of}\:\mathrm{unit}\:\mathrm{area}. \\ $$ Commented by mr W last updated on…

Towns-A-B-C-and-D-are-located-on-the-vertices-of-a-square-whose-area-is-1000km-2-There-is-a-straight-line-highway-passing-through-the-centre-of-the-square-but-not-through-any-of-the-towns-Find-the-

Question Number 111278 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{Towns}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{and}\:\mathrm{D}\:\mathrm{are}\:\mathrm{located}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{whose}\:\mathrm{area}\:\mathrm{is} \\ $$$$\mathrm{1000km}^{\mathrm{2}} .\:\mathrm{There}\:\mathrm{is}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{highway}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{square}\:\mathrm{but}\:\mathrm{not}\:\mathrm{through}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{towns}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{squares} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{distances}\:\mathrm{of}\:\mathrm{the}\:\mathrm{towns}\:\mathrm{to}\:\mathrm{the}…

Triangle-ABC-has-AB-2-AC-Let-D-and-E-be-on-AB-and-BC-respectively-such-that-BAE-ACD-Let-F-be-the-intersections-of-segments-AE-and-CD-and-suppose-that-CFE-is-equilateral-What-is-ACB-

Question Number 111279 by Aina Samuel Temidayo last updated on 03/Sep/20 $$\mathrm{Triangle}\:\mathrm{ABC}\:\mathrm{has}\:\mathrm{AB}=\mathrm{2}\centerdot\mathrm{AC}.\:\mathrm{Let} \\ $$$$\mathrm{D}\:\mathrm{and}\:\mathrm{E}\:\mathrm{be}\:\mathrm{on}\:\mathrm{AB}\:\mathrm{and}\:\mathrm{BC} \\ $$$$\mathrm{respectively}\:\mathrm{such}\:\mathrm{that}\:\angle\mathrm{BAE} \\ $$$$=\angle\mathrm{ACD}.\:\mathrm{Let}\:\mathrm{F}\:\mathrm{be}\:\mathrm{the}\:\mathrm{intersections}\:\mathrm{of} \\ $$$$\mathrm{segments}\:\mathrm{AE}\:\mathrm{and}\:\mathrm{CD},\:\mathrm{and}\:\mathrm{suppose} \\ $$$$\mathrm{that}\:\bigtriangleup\mathrm{CFE}\:\mathrm{is}\:\mathrm{equilateral}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\angle\mathrm{ACB}? \\…