# A chord with a length of #14 # runs from #pi/3 # to #pi/2 # radians on a circle. What is the area of the circle?

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To find the area of the circle, we need to know the radius. Since we have a chord length and the angle it subtends, we can use trigonometry to find the radius.

- First, note that the chord divides the circle into two segments, with one being a minor segment and the other being a major segment.
- The chord length is the straight-line distance between the two points where the chord intersects the circle.
- Using trigonometry, we can find half the chord length, which is the distance from the center of the circle to the midpoint of the chord.
- This distance is ( r\sin(\frac{\theta}{2}) ), where ( r ) is the radius and ( \theta ) is the angle subtended by the chord.

- Since the chord runs from ( \frac{\pi}{3} ) to ( \frac{\pi}{2} ) radians, the angle subtended by the chord is ( \frac{\pi}{2} - \frac{\pi}{3} = \frac{\pi}{6} ).
- Now, we have half the chord length, which is ( 7 ) (since the full chord length is ( 14 )).
- Solve for ( r ) using ( 7 = r\sin\left(\frac{\pi}{6}\right) ).
- ( r = \frac{7}{\sin\left(\frac{\pi}{6}\right)} ).

- Once you find the radius, ( r ), you can calculate the area of the circle using the formula ( A = \pi r^2 ).

Performing these calculations will give you the area of the circle.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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