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GeometryQuestion and Answers: Page 88

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A and B are two points from the plan (P) with AB=4 define and draw the locus of points M ∈(P) wich verify MA +MB =8 .

$${A}\:{and}\:{B}\:{are}\:{two}\:{points}\:{from}\:{the}\:{plan}\:\left({P}\right)\:{with}\:{AB}=\mathrm{4}\:{define}\:{and}\:{draw} \\ $$$${the}\:{locus}\:{of}\:{points}\:{M}\:\in\left({P}\right)\:{wich}\:{verify}\:\:\:{MA}\:+{MB}\:=\mathrm{8}\:. \\ $$

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Find the maximum area of a triangle inscribed in an ellipse with parameters a and b.

$${Find}\:{the}\:{maximum}\:{area}\:{of}\:{a}\:{triangle} \\ $$$${inscribed}\:{in}\:{an}\:{ellipse}\:{with}\:{parameters} \\ $$$${a}\:{and}\:{b}. \\ $$

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Question Number 50352    Answers: 1   Comments: 5

The distances from a point to the sides of a triangle are p,q,r. Find the maximum (or minimum) area of the triangle, if it exists. Assume r≤q≤p.

$${The}\:{distances}\:{from}\:{a}\:{point}\:{to}\:{the}\:{sides} \\ $$$${of}\:{a}\:{triangle}\:{are}\:{p},{q},{r}.\:{Find}\:{the}\: \\ $$$${maximum}\:\left({or}\:{minimum}\right)\:{area}\:{of}\:{the} \\ $$$${triangle},\:{if}\:{it}\:{exists}. \\ $$$${Assume}\:{r}\leqslant{q}\leqslant{p}. \\ $$

Question Number 49987    Answers: 1   Comments: 4

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Question Number 49736    Answers: 1   Comments: 1

there is two small and one grater circles that [two]are tangent to [one]and all three circles are inscribed in an ellipse with: [(a/b)=2(√2)]and tangent to it at two points such that center of circles are on major axe of ellipse. find: ((radi of great circle)/(radi of small circle)) .

$$\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{small}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{grater}}\:\boldsymbol{\mathrm{circles}} \\ $$$$\boldsymbol{\mathrm{that}}\:\left[\boldsymbol{\mathrm{two}}\right]\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{tangent}}\:\boldsymbol{\mathrm{to}}\:\left[\boldsymbol{\mathrm{one}}\right]\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{three}} \\ $$$$\:\boldsymbol{\mathrm{circles}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{ellipse}}\:\boldsymbol{\mathrm{with}}: \\ $$$$\left[\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}=\mathrm{2}\sqrt{\mathrm{2}}\right]\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{tangent}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{points}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{center}}\: \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{circles}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axe}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{ellipse}}. \\ $$$$\boldsymbol{\mathrm{find}}:\:\:\:\:\frac{\boldsymbol{\mathrm{radi}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{great}}\:\boldsymbol{\mathrm{circle}}}{\boldsymbol{\mathrm{radi}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{small}}\:\boldsymbol{\mathrm{circle}}}\:\:. \\ $$

Question Number 49731    Answers: 1   Comments: 0

one vertex of a equilateral triangle lies on one vertex of a square and two anothers lie on opposite sides of square such that triangle have the maximum area. find: 1.ratio of: ((square side)/(triangle side)) 2.angle between square side and triangle side.[need additional data?]

$$\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{vertex}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{equilateral}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{lies}} \\ $$$$\boldsymbol{\mathrm{on}}\:\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{vertex}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{two}} \\ $$$$\boldsymbol{\mathrm{anothers}}\:\boldsymbol{\mathrm{lie}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{opposite}}\:\boldsymbol{\mathrm{sides}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{square}} \\ $$$$\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{maximum}} \\ $$$$\boldsymbol{\mathrm{area}}. \\ $$$$\boldsymbol{\mathrm{find}}: \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{ratio}}\:\boldsymbol{\mathrm{of}}:\:\:\:\:\:\frac{\boldsymbol{\mathrm{square}}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{side}}}{\boldsymbol{\mathrm{triangle}}\:\:\:\:\:\:\:\boldsymbol{\mathrm{side}}} \\ $$$$\mathrm{2}.\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{between}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{side}}.\left[\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{additional}}\:\boldsymbol{\mathrm{data}}?\right] \\ $$

Question Number 49730    Answers: 0   Comments: 1

find the largest ellipse inscribed in a given rectangle and its major axe of:ellipse lies on rectangle diagonal.

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{ellipse}}\:\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{rectangle}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axe}}\:\boldsymbol{\mathrm{of}}:\boldsymbol{\mathrm{ellipse}} \\ $$$$\boldsymbol{\mathrm{lies}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{rectangle}}\:\boldsymbol{\mathrm{diagonal}}. \\ $$

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