Question Number 15440 by mrW1 last updated on 10/Jun/17 Commented by mrW1 last updated on 10/Jun/17 $$\mathrm{The}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral} \\ $$$$\mathrm{ABCD}\:\mathrm{are}\:\mathrm{elongated}\:\mathrm{2}\:\mathrm{times}\:\mathrm{in}\:\mathrm{one} \\ $$$$\mathrm{direction},\:\mathrm{see}\:\mathrm{diagram},\:\mathrm{to}\:\mathrm{form}\:\mathrm{a}\:\mathrm{new} \\ $$$$\mathrm{quadrilateral}\:\mathrm{EFGH}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{quadrilateral}\:\mathrm{if}\:\mathrm{the}…
Question Number 15434 by mrW1 last updated on 10/Jun/17 Commented by mrW1 last updated on 10/Jun/17 $$\mathrm{Two}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{radius}\:\mathrm{6}\:\mathrm{and}\:\mathrm{10}\:\mathrm{and} \\ $$$$\mathrm{center}\:\mathrm{at}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{intersect}\:\mathrm{at}\:\mathrm{point}\:\mathrm{C} \\ $$$$\mathrm{and}\:\mathrm{D}.\:\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{is}\:\mathrm{12}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{max}.\:\mathrm{length}\:\mathrm{of} \\ $$$$\mathrm{segment}\:\mathrm{EF}\:\mathrm{through}\:\mathrm{C}?…
Question Number 146494 by syamilkamil1 last updated on 13/Jul/21 $$ \\ $$$$\mathrm{Solid}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{pla}{ne}\:{X}\:\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{forms}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{slices}\: \\ $$$$\mathrm{IJK}{LM}\mathrm{N}\:\mathrm{where}\:\mathrm{I}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{AB},\:\mathrm{J}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{BF} \\ $$$$\:{K}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{FG},\:\:\mathrm{L}\:\mathrm{is}\:\mathrm{mid}\:\mathrm{HG},\:\:\mathrm{M}\:\mathrm{mid}\:\mathrm{DH}\: \\ $$$$\mathrm{and}\:\mathrm{N}\:\mathrm{mid}\:\mathrm{AD}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{edge}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\: \\ $$$$\mathrm{is}\:{X},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{IJKLMN}\:\mathrm{field} \\ $$ Terms…
Question Number 146487 by syamilkamil1 last updated on 13/Jul/21 $$ \\ $$$$\mathrm{Cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{has}\:\mathrm{side}\:\mathrm{length}\:\mathrm{a}. \\ $$$$\mathrm{P}{o}\mathrm{int}\:\mathrm{P}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{AC}\:\mathrm{such}\:\mathrm{that}\:\mathrm{AP}\::\:\mathrm{PC}\:=\:\mathrm{3}\::\:\mathrm{1}\:\mathrm{Through}\:\mathrm{P}\:\mathrm{a}\:\mathrm{line}\:\mathrm{l}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{BD}\:\mathrm{is} \\ $$$$\mathrm{dr}{a}\mathrm{wn}\:\mathrm{such}\:\mathrm{that}\:\mathrm{l}\:\mathrm{each}\:\mathrm{intersect}\:\mathrm{BC}\:\mathrm{at}\: \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{CD}\:\mathrm{at}\:\mathrm{Y}.\:\mathrm{If}\:\mathrm{AC}\:\mathrm{and}\:\mathrm{BD}\: \\ $$$$\mathrm{intersect}\:\mathrm{at}\:\mathrm{O}\:\mathrm{find}\:\mathrm{the}\:\mathrm{distance}\: \\ $$$$\mathrm{between}\:\mathrm{XY}\:\mathrm{with}\:\mathrm{OG}! \\ $$ Terms…
Question Number 15318 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 09/Jun/17 Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 09/Jun/17 $${given}:\:{ABCD},{rectangle}.{connect}\: \\ $$$${each}\:{vertex}\:{to}\:{the}\:{middle}\:{point}\:{of} \\ $$$${one}\:{other}\:{sides}\:{as}\:{shown}. \\ $$$$\left.\mathrm{1}\right){show}\:{that}\:{MNPQ},{is}\:{a}\:{parallelogram} \\ $$$${and}\:{its}\:{area}\:{is}\:{equail}\:{to}:\:\frac{\mathrm{1}}{\mathrm{5}}{area}\:{of}\:{ABCD}.…
Question Number 80809 by mr W last updated on 06/Feb/20 Commented by mr W last updated on 06/Feb/20 $${I}\:{is}\:{a}\:{point}\:{inside}\:{the}\:{triangle}\:{ABC}. \\ $$$${P},{Q},{R}\:{are}\:{the}\:{midpoint}\:{of}\:{AI},{BI},{CI} \\ $$$${respectively}. \\ $$$${What}\:{fraction}\:{of}\:{the}\:{triangle}\:{ABC}…
Question Number 80795 by mr W last updated on 06/Feb/20 Commented by mr W last updated on 06/Feb/20 $${Find}\:{the}\:{equation}\:{of}\:{the}\:{parabola},\:{i}.{e}. \\ $$$${the}\:{value}\:{k}\:{as}\:{well}\:{as}\:{the}\:{corresponding} \\ $$$${coordinates}\:{of}\:{points}\:{A},{B},{C}\:{such}\:{that} \\ $$$${the}\:{areas}\:{I},\:{II},\:{III},\:{IV}\:\:{are}\:{equal}.…
Question Number 80761 by Power last updated on 06/Feb/20 Commented by Power last updated on 06/Feb/20 $$\mathrm{AD}−\mathrm{BE}−\mathrm{FC}−\mathrm{Height}\:\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\angle\mathrm{F}=?\:\:\:\:\:\:\:\angle\mathrm{E}=? \\ $$ Terms of Service Privacy…
Question Number 15212 by ajfour last updated on 08/Jun/17 Commented by ajfour last updated on 08/Jun/17 $${Solution}\:{to}\:{Q}.\mathrm{15175} \\ $$ Answered by ajfour last updated on…
Question Number 80731 by ajfour last updated on 05/Feb/20 Commented by ajfour last updated on 05/Feb/20 $${The}\:{pentagon}\:{has}\:{each}\:{side}\:{s}. \\ $$$${Find}\:{s},\:{in}\:{terms}\:{of}\:{ellipse} \\ $$$${parameters}\:{a}\:{and}\:{b}. \\ $$ Answered by…