Question Number 49830 by ajfour last updated on 11/Dec/18 Commented by ajfour last updated on 11/Dec/18 $${Find}\:{circumradius}\:\boldsymbol{{r}}\:{in}\:{terms}\:{of}\:\boldsymbol{{a}}. \\ $$ Answered by mr W last updated…
Question Number 180897 by depressiveshrek last updated on 18/Nov/22 Commented by depressiveshrek last updated on 18/Nov/22 $$\mid{AB}\mid=\mathrm{3} \\ $$$$\mid{BC}\mid=\mathrm{5} \\ $$$${BE}={EC} \\ $$$$\mid{CD}\mid=\mathrm{1} \\ $$$${Find}\:{the}\:{area}\:{of}\:{the}\:{white}\:\left({not}\:{the}\:{gray}\:{one}\right)\:{area}…
Question Number 180882 by mr W last updated on 18/Nov/22 Commented by mr W last updated on 18/Nov/22 $${prove}\:{that}\:{the}\:{lengthes}\:{of}\:{the}\:{blue} \\ $$$${lines}\:{are}\:\mathrm{4}\:{times}\:{of}\:{the} \\ $$$${corresponding}\:{side}\:{lengthes}\:{of}\:{the} \\ $$$${triangle}.…
Question Number 49748 by Pk1167156@gmail.com last updated on 10/Dec/18 Answered by MJS last updated on 11/Dec/18 $$\mid{AB}\mid=\mathrm{2}{a} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{2}{a}^{\mathrm{2}} \:\Rightarrow\:{y}_{\mathrm{1}} =\sqrt{\mathrm{2}{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }…
Question Number 180813 by mr W last updated on 17/Nov/22 Commented by mr W last updated on 17/Nov/22 $${the}\:{areas}\:{of}\:{three}\:{squares}\:{are}\:{given}. \\ $$$${find}\:{the}\:{areas}\:{of}\:{the}\:{three}\:{blue}\: \\ $$$${squares}. \\ $$…
Question Number 49736 by behi83417@gmail.com last updated on 10/Dec/18 $$\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{small}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{grater}}\:\boldsymbol{\mathrm{circles}} \\ $$$$\boldsymbol{\mathrm{that}}\:\left[\boldsymbol{\mathrm{two}}\right]\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{tangent}}\:\boldsymbol{\mathrm{to}}\:\left[\boldsymbol{\mathrm{one}}\right]\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{three}} \\ $$$$\:\boldsymbol{\mathrm{circles}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{ellipse}}\:\boldsymbol{\mathrm{with}}: \\ $$$$\left[\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}=\mathrm{2}\sqrt{\mathrm{2}}\right]\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{tangent}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{points}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{center}}\: \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circles}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axe}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{ellipse}}. \\ $$$$\boldsymbol{\mathrm{find}}:\:\:\:\:\frac{\boldsymbol{\mathrm{radi}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{great}}\:\boldsymbol{\mathrm{circle}}}{\boldsymbol{\mathrm{radi}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{small}}\:\boldsymbol{\mathrm{circle}}}\:\:. \\ $$ Commented by ajfour…
Question Number 49731 by behi83417@gmail.com last updated on 09/Dec/18 $$\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{vertex}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{equilateral}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{lies}} \\ $$$$\boldsymbol{\mathrm{on}}\:\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{vertex}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{two}} \\ $$$$\boldsymbol{\mathrm{anothers}}\:\boldsymbol{\mathrm{lie}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{opposite}}\:\boldsymbol{\mathrm{sides}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{square}} \\ $$$$\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{maximum}} \\ $$$$\boldsymbol{\mathrm{area}}. \\ $$$$\boldsymbol{\mathrm{find}}: \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{ratio}}\:\boldsymbol{\mathrm{of}}:\:\:\:\:\:\frac{\boldsymbol{\mathrm{square}}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{side}}}{\boldsymbol{\mathrm{triangle}}\:\:\:\:\:\:\:\boldsymbol{\mathrm{side}}} \\ $$$$\mathrm{2}.\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{between}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{triangle}} \\…
Question Number 49730 by behi83417@gmail.com last updated on 09/Dec/18 $$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{ellipse}}\:\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{rectangle}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axe}}\:\boldsymbol{\mathrm{of}}:\boldsymbol{\mathrm{ellipse}} \\ $$$$\boldsymbol{\mathrm{lies}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{rectangle}}\:\boldsymbol{\mathrm{diagonal}}. \\ $$ Commented by mr W last updated on 10/Dec/18 $${I}\:{don}'{t}\:{think}\:{there}\:{exists}\:{such}\:{an}\:{inscribed}…
Question Number 49725 by behi83417@gmail.com last updated on 09/Dec/18 Commented by behi83417@gmail.com last updated on 09/Dec/18 $${ABC},{is}\:{equilaterl}.\frac{{AD}}{{DB}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\measuredangle{ADC}=? \\ $$ Answered by ajfour last…
Question Number 49696 by ajfour last updated on 09/Dec/18 Commented by ajfour last updated on 09/Dec/18 $${Find}\:{parameters}\:{of}\:{ellipse}\:{within} \\ $$$${the}\:{box}\:{and}\:{touching}\:{all}\:{its}\:{six} \\ $$$${faces}\:{at}\:{A},\:{B},\:{C},\:{D},\:{E},\:{and}\:{F}\:\:{and} \\ $$$$\left({may}\:{be}\:{for}\:{uniqueness}\right)\:{of} \\ $$$${maximum}\:{area}.…