A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{π}{2}$ $pi/2$ radians on the circle. If the area of the circle is $48 π$ $48 pi$ , what is the length of the chord?

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Answer 1 · 2017-10-16T10:50:12

The length of a chord is $5.30$ $5.30$ unit.

Formula for the length of a chord is $L_{c} = 2 r sin (\frac{θ}{2})$ $L_c= 2r sin (theta/2)$

where $r$ $r$ is the radius of the circle and $θ$ $theta$ is the angle

subtended at the center by the chord. Area of circle is

$cancelpi * r^2 = 48 cancelpi :. r^2 = 48 or r = sqrt48 =4 sqrt3$

$theta= pi/2-pi/4 = pi/4 :. L_c= 2 *4sqrt3 *sin ((pi/4)/2)$ or

$L_c= 2 * 4sqrt3 * sin (pi//8) = 8 sqrt3 * sin 22.5 [pi/8=22.5^0]$ or

$L_c= 5.30$ unit. The length of a chord is $5.30$ unit.[Ans]

A circle has a chord that goes from pi/4 π4pi/4 to pi/2 π2pi/2 radians on the circle. If the area of the circle is 48 pi 48π48 pi , what is the length of the chord?