A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{3 π}{4}$ $(3 pi) / 4$ radians on the circle. If the area of the circle is $196 π$ $196 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{3 π}{4}$ $(3 pi) / 4$ radians on the circle. If the area of the circle is $196 π$ $196 pi$ , what is the length of the chord?

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Answer 1 · 2017-08-17T10:23:10

$\approx 10.72$ $~~ 10.72$

Explanation:

$∙ the area of a circle = π r^{2}$ $• " the area of a circle "=pir^2$

$\Rightarrow π r^{2} = 196 π$ $rArrpir^2=196pi$

$rArrr^2=(196cancel(pi))/cancel(pi)=196$

$rArrr=sqrt196=14$

$"the angle subtended at the centre of the circle by the"$
$"chord is"$

$(3pi)/4-pi/2=(3pi)/4-(2pi)/4=pi/4$

$"we now have a triangle made up of the 2 radii and the"$
$"chord "$

$"to find length of chord use the "color(blue)"cosine rule"$

$•color(white)(x)c^2=a^2+b^2-2abcosC$

$"where "a=b=14" and "angleC=pi/4$

$c^2=14^2+14^2-(2xx14xx14xxcos(pi/4))$

$color(white)(c^2)~~ 114.814$

$rArrc=sqrt114.814~~ 10.72" to 2 dec. places"$

$rArr"length of chord "~~ 10.72$

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{3 π}{4}$ $(3 pi) / 4$ radians on the circle. If the area of the circle is $196 π$ $196 pi$ , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from ( pi)/2 π2( pi)/2 to (3 pi) / 4 3π4(3 pi) / 4 radians on the circle. If the area of the circle is 196 pi 196π196 pi , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from $\frac{π}{2}$ $( pi)/2$ to $\frac{3 π}{4}$ $(3 pi) / 4$ radians on the circle. If the area of the circle is $196 π$ $196 pi$ , what is the length of the chord?