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Category: Geometry

Question-175166

Question Number 175166 by cherokeesay last updated on 21/Aug/22 Answered by ajfour last updated on 22/Aug/22 $${let}\:{centre}\:{of}\:{required}\:{circle} \\ $$$${be}\:\:\left({h},{R}\right) \\ $$$${h}=−\frac{{r}}{\mathrm{2}\sqrt{\mathrm{2}}}=−\mathrm{4} \\ $$$$\Rightarrow\:\:{r}=\mathrm{8}\sqrt{\mathrm{2}} \\ $$$$\left({h}−\frac{{r}}{\:\sqrt{\mathrm{2}}}\right)^{\mathrm{2}}…

An-isosceles-AEF-is-inscribed-into-a-square-ABCD-such-that-pointE-is-on-side-BC-point-F-is-on-side-CDand-AE-EF-Knownthat-tanAEF-2-Find-tanFEC-

Question Number 109591 by 1549442205PVT last updated on 25/Aug/20 $$\mathrm{An}\:\mathrm{isosceles}\:\mathrm{AEF}\:\mathrm{is}\:\mathrm{inscribed}\:\mathrm{into}\:\mathrm{a} \\ $$$$\mathrm{square}\:\mathrm{ABCD}\:\mathrm{such}\:\mathrm{that}\:\mathrm{pointE}\:\mathrm{is}\:\mathrm{on} \\ $$$$\mathrm{side}\:\mathrm{BC},\mathrm{point}\:\mathrm{F}\:\mathrm{is}\:\mathrm{on}\:\mathrm{side}\:\mathrm{CDand}\:\mathrm{AE}=\mathrm{EF}. \\ $$$$\mathrm{Knownthat}\:\mathrm{tan}\widehat {\mathrm{AEF}}=\mathrm{2}.\mathrm{Find}\:\mathrm{tan}\widehat {\mathrm{FEC}} \\ $$ Commented by 1549442205PVT last updated…

Question-44017

Question Number 44017 by ajfour last updated on 20/Sep/18 Commented by ajfour last updated on 20/Sep/18 $${A}\:{cone}\:{is}\:{cut}\:{by}\:{a}\:{plane}\:\:{at}\:{an} \\ $$$${angle}\:\theta\:{to}\:{its}\:{base}\:{and}\:{passes} \\ $$$${through}\:{a}\:{point}\:{at}\:{the}\:{base}\:{of} \\ $$$${cone}.\:{Find}\:{ratio}\:{of}\:\boldsymbol{{upper}}\:\boldsymbol{{cone}} \\ $$$$\boldsymbol{{volume}}\:\boldsymbol{{to}}\:\boldsymbol{{lower}}\:\boldsymbol{{cone}}\:\boldsymbol{{volume}}.…

Question-109508

Question Number 109508 by Study last updated on 24/Aug/20 Commented by som(math1967) last updated on 24/Aug/20 $$\:\frac{\mathrm{1}}{\mathrm{4}}\pi×\mathrm{2}^{\mathrm{2}} −\left\{\frac{\mathrm{1}}{\mathrm{2}}\pi×\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{1}×\mathrm{1}\right\} \\ $$$$\left(\pi−\frac{\pi}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{cm}^{\mathrm{2}} \\ $$ Answered by…

In-the-figure-ABCD-is-an-square-and-BM-MC-If-the-area-of-PCD-14u-What-is-the-value-of-1-Area-of-ABC-2-Area-of-ABMP-3-The-area-of-ABCD-

Question Number 175045 by 2kdw last updated on 17/Aug/22 $${In}\:{the}\:{figure}\:{ABCD}\:{is}\:{an}\:{square}\:{and} \\ $$$${BM}={MC}.\:{If}\:{the}\:{area}\:{of}\:{PCD}=\mathrm{14}{u}.\: \\ $$$${What}\:{is}\:{the}\:{value}\:{of}: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{Area}\:{of}\:{ABC}; \\ $$$$\left(\mathrm{2}\right)\:{Area}\:{of}\:\:{ABMP}; \\ $$$$\left(\mathrm{3}\right)\:{The}\:{area}\:{of}\:{ABCD} \\ $$$$ \\…

If-the-points-3-5-4-2-and-6-2-are-the-vertices-of-a-triangle-i-Find-the-equation-of-the-perpendicular-bisector-of-the-sides-ii-Find-the-coordinate-of-the-circumcenter-The-circumcen

Question Number 43944 by Tawa1 last updated on 18/Sep/18 $$\mathrm{If}\:\mathrm{the}\:\mathrm{points}\:\left(−\mathrm{3},\:\mathrm{5}\right)\:,\:\left(\mathrm{4},\:−\mathrm{2}\right)\:\mathrm{and}\:\left(\mathrm{6},\:\mathrm{2}\right)\:\mathrm{are}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{perpendicular}\:\mathrm{bisector}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumcenter}.\:\left(\mathrm{The}\:\mathrm{circumcenter}\:\mathrm{of}\:\mathrm{a}\right. \\ $$$$\mathrm{triangle}\:\mathrm{is}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{of}\:\mathrm{the}\:\mathrm{perpendicular}\:\mathrm{bisector}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{side} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circumcircle}. \\ $$ Answered by tanmay.chaudhury50@gmail.com…