# A circle has a chord that goes from #( 2 pi)/3 # to #(11 pi) / 12 # radians on the circle. If the area of the circle is #12 pi #, what is the length of the chord?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the length of the chord, you can use the formula:

[ \text{Chord length} = 2 \times \text{radius} \times \sin\left(\frac{\text{central angle}}{2}\right) ]

First, calculate the radius of the circle using the formula for the area of a circle:

[ \text{Area} = \pi r^2 ]

[ 12\pi = \pi r^2 ]

[ r^2 = 12 ]

[ r = \sqrt{12} = 2\sqrt{3} ]

Now, find the central angle:

[ \text{Central angle} = \left(\frac{11\pi}{12}\right) - \left(\frac{2\pi}{3}\right) = \frac{11\pi}{12} - \frac{8\pi}{12} = \frac{3\pi}{12} = \frac{\pi}{4} ]

Now, plug the values into the formula for the chord length:

[ \text{Chord length} = 2 \times 2\sqrt{3} \times \sin\left(\frac{\pi}{8}\right) ]

[ \text{Chord length} = 4\sqrt{3} \times \sin\left(\frac{\pi}{8}\right) ]

[ \text{Chord length} \approx 4\sqrt{3} \times 0.3827 ]

[ \text{Chord length} \approx 1.5308 \times 4\sqrt{3} ]

[ \text{Chord length} \approx 6.123 ]

So, the length of the chord is approximately (6.123) units.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- A circle's center is at #(2 ,4 )# and it passes through #(3 ,1 )#. What is the length of an arc covering #(13pi ) /8 # radians on the circle?
- A circle has a chord that goes from #( 5 pi)/4 # to #(5 pi) / 3 # radians on the circle. If the area of the circle is #42 pi #, what is the length of the chord?
- A circle has a chord that goes from #( 3 pi)/4 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #81 pi #, what is the length of the chord?
- A triangle has corners at #(3 , 8 )#, #(4 ,2 )#, and #(2 ,1 )#. What is the radius of the triangle's inscribed circle?
- The diameter of two cylinder are in the ratio of 2:3. What will be the ratio of their heights if their volumes are equal ?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7