A circle has a chord that goes from $( pi)/2$ to $(13 pi) / 6$ radians on the circle. If the area of the circle is $5 pi$ , what is the length of the chord?

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A circle has a chord that goes from $( pi)/2$ to $(13 pi) / 6$ radians on the circle. If the area of the circle is $5 pi$ , what is the length of the chord?

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Answer 1 · 2018-06-27T14:57:35

The length of the chord is $sqrt5$ .

Explanation:

Let the center of the circle be point $O$ . Let the point at $pi/2$ be point $A$ and let the point at $(13pi)/6$ be point $B$ . Since $(13pi)/6=2pi+pi/6$ , point $B$ can be thought of as located at an angle of $pi/6$ . Therefore, $m/_AOB=pi/2-pi/6=pi/3$ . Since points $A$ and $B$ are located on the circle, $OA=OB$ because they are both radii. Since $OA=OB$ , we know that $m/_OAB=m/_OBA$ and since $m/_AOB=pi/3$ , we know that $m/_OAB=m/_OBA=m/_AOB=pi/3$ and that $OA=OB=AB$ .

The area of a circle is given by $A=pir^2$ so we know $5pi=pir^2$ or that $r=sqrt5$ . Since $OA=r=sqrt5$ and chord $AB=OA$ , $AB=sqrt5$ .

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A circle has a chord that goes from $( pi)/2$ to $(13 pi) / 6$ radians on the circle. If the area of the circle is $5 pi$ , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from ( pi)/2 ( pi)/2 to (13 pi) / 6 (13 pi) / 6 radians on the circle. If the area of the circle is 5 pi 5 pi , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from $( pi)/2$ to $(13 pi) / 6$ radians on the circle. If the area of the circle is $5 pi$ , what is the length of the chord?