Category: Geometry

Question Number 180897 by depressiveshrek last updated on 18/Nov/22 Commented by depressiveshrek last updated on 18/Nov/22 $$\mid AB\mid =3$$$$\mid BC\mid =5$$$$BE=EC$$$$\mid CD\mid =1$$$${Find}\:{the}\:{area}\:{of}\:{the}\:{white}\:\left({not}\:{the}\:{gray}\:{one}\right)\:{area}…

Question Number 49748 by Pk1167156@gmail.com last updated on 10/Dec/18 Answered by MJS last updated on 11/Dec/18 $$\mid AB\mid =2a$$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}{a}^{\mathrm{2}} \:\Rightarrow\:{y}_{\mathrm{1}} =\sqrt{\mathrm{2}{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }…

Question Number 49736 by behi83417@gmail.com last updated on 10/Dec/18 $$\mathbf{there}\mathbf{is}\mathbf{two}\mathbf{small}\mathbf{and}\mathbf{one}\mathbf{grater}\mathbf{circles}$$$$\mathbf{that}\left[\mathbf{two}\right]\mathbf{are}\mathbf{tangent}\mathbf{to}\left[\mathbf{one}\right]\mathbf{and}\mathbf{all}\mathbf{three}$$$$\mathbf{circles}\mathbf{are}\mathbf{inscribed}\mathbf{in}\mathbf{an}\mathbf{ellipse}\mathbf{with}:$$$$[\frac{\mathbf{a}}{\mathbf{b}}=2\sqrt{2}]\mathbf{and}\mathbf{tangent}\mathbf{to}\mathbf{it}\mathbf{at}\mathbf{two}\mathbf{points}\mathbf{such}\mathbf{that}\mathbf{center}$$$$\mathbf{of}\mathbf{circles}\mathbf{are}\mathbf{on}\mathbf{major}\mathbf{axe}\mathbf{of}\mathbf{ellipse}.$$$$\mathbf{find}:\frac{\mathbf{radi}\mathbf{of}\mathbf{great}\mathbf{circle}}{\mathbf{radi}\mathbf{of}\mathbf{small}\mathbf{circle}}.$$ Commented by ajfour…

Question Number 49730 by behi83417@gmail.com last updated on 09/Dec/18 $$\mathbf{find}\mathbf{the}\mathbf{largest}\mathbf{ellipse}\mathbf{inscribed}\mathbf{in}\mathbf{a}$$$$\mathbf{given}\mathbf{rectangle}\mathbf{and}\mathbf{its}\mathbf{major}\mathbf{axe}\mathbf{of}:\mathbf{ellipse}$$$$\mathbf{lies}\mathbf{on}\mathbf{rectangle}\mathbf{diagonal}.$$ Commented by mr W last updated on 10/Dec/18 $${I}\:{don}'{t}\:{think}\:{there}\:{exists}\:{such}\:{an}\:{inscribed}…

Question Number 49696 by ajfour last updated on 09/Dec/18 Commented by ajfour last updated on 09/Dec/18 $$Findparametersofellipsewithin$$$$theboxandtouchingallitssix$$$$facesatA,B,C,D,E,andFand$$$$\left(maybeforuniqueness\right)of$$$${maximum}\:{area}.…