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GeometryQuestion and Answers: Page 94

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Find radius c in terms of radii a and b.

$${Find}\:{radius}\:{c}\:{in}\:{terms}\:{of}\:{radii} \\ $$$${a}\:{and}\:{b}. \\ $$

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Prove that if circum-circle and in-circle of a triangle are concentric, the triangle is an equalateral triangle.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:\boldsymbol{\mathrm{circum}}-\boldsymbol{\mathrm{circle}}\:\mathrm{and} \\ $$$$\boldsymbol{\mathrm{in}}-\boldsymbol{\mathrm{circle}}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\boldsymbol{\mathrm{concentric}}, \\ $$$$\mathrm{the}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{an}\:\boldsymbol{\mathrm{equalateral}}\:\boldsymbol{\mathrm{triangle}}. \\ $$

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2∧6

$$\mathrm{2}\wedge\mathrm{6} \\ $$

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2 lines through the point A(5, 1) are tangent to the circle x^2 + y^2 − 4x + 6y + 4 = 0 Find the equation of these 2 lines

$$\mathrm{2}\:\mathrm{lines}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:{A}\left(\mathrm{5},\:\mathrm{1}\right)\:\mathrm{are}\:\mathrm{tangent} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{circle}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\:\mathrm{4}{x}\:+\:\mathrm{6}{y}\:+\:\mathrm{4}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{these}\:\mathrm{2}\:\mathrm{lines} \\ $$

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if ΔABC similar ΔPQR and area of ΔPQR=4area(ΔABC) then AB:PQ is

$$\mathrm{if}\:\Delta\mathrm{ABC}\:\mathrm{similar}\:\Delta\mathrm{PQR}\:\mathrm{and}\:\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{PQR}=\mathrm{4area}\left(\Delta\mathrm{ABC}\right)\:\mathrm{then}\:\mathrm{AB}:\mathrm{PQ}\:\mathrm{is} \\ $$

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derive the equation of a chain of length l mass m hanging between two points x distance apart.

$${derive}\:{the}\:{equation}\:{of}\:{a}\:{chain} \\ $$$${of}\:{length}\:{l}\:{mass}\:{m}\:{hanging} \\ $$$${between}\:{two}\:{points}\:{x}\:{distance} \\ $$$${apart}. \\ $$

Question Number 29321 Answers: 0 Comments: 1

is it possible to divide an angle into three equal parts?

$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{divide}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{into}\:\mathrm{three}\:\mathrm{equal}\:\mathrm{parts}? \\ $$

Question Number 29116 Answers: 1 Comments: 0

Find the area of the region R bounded by the curve y = cosh(x), the line x = log_e (2) and the coordinate axis . Find also the volume obtained when R is rotated completely about the x − axis.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\boldsymbol{\mathrm{R}}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curve}\:\:\mathrm{y}\:=\:\mathrm{cosh}\left(\mathrm{x}\right),\:\:\mathrm{the}\:\mathrm{line}\:\:\mathrm{x}\:=\:\mathrm{log}_{\mathrm{e}} \left(\mathrm{2}\right) \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{coordinate}\:\mathrm{axis}\:.\:\:\mathrm{Find}\:\mathrm{also}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{obtained}\:\mathrm{when}\:\boldsymbol{\mathrm{R}}\:\mathrm{is}\:\mathrm{rotated}\: \\ $$$$\mathrm{completely}\:\mathrm{about}\:\mathrm{the}\:\:\mathrm{x}\:−\:\mathrm{axis}. \\ $$

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Testing of a Bakelite sample by schering Bridge having a standard capacitor of 106pF , balance was obtained with a capacitance of 0.351 F in parallel with non - inductive resistance in the remaining arm of the bridge being 130 Ω. Determine the capacitance and the equivalent series resistance of the specimen and draw the circuit diagram.

$$\mathrm{Testing}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Bakelite}\:\mathrm{sample}\:\mathrm{by}\:\mathrm{schering}\:\mathrm{Bridge}\:\mathrm{having}\:\mathrm{a}\:\mathrm{standard}\:\mathrm{capacitor} \\ $$$$\mathrm{of}\:\:\mathrm{106pF}\:,\:\:\mathrm{balance}\:\mathrm{was}\:\mathrm{obtained}\:\mathrm{with}\:\mathrm{a}\:\mathrm{capacitance}\:\mathrm{of}\:\:\:\mathrm{0}.\mathrm{351}\:\mathrm{F}\:\:\mathrm{in}\:\mathrm{parallel} \\ $$$$\mathrm{with}\:\mathrm{non}\:-\:\mathrm{inductive}\:\mathrm{resistance}\:\mathrm{in}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{arm}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bridge}\:\mathrm{being}\:\:\:\mathrm{130}\:\Omega. \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{capacitance}\:\mathrm{and}\:\mathrm{the}\:\mathrm{equivalent}\:\mathrm{series}\:\mathrm{resistance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{specimen} \\ $$$$\mathrm{and}\:\mathrm{draw}\:\mathrm{the}\:\mathrm{circuit}\:\mathrm{diagram}. \\ $$

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