# A circle has a chord that goes from #( 11 pi)/6 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #128 pi #, what is the length of the chord?

See below.

Hopefully this helps :).

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

To find the length of the chord, use the formula for the length of a chord in a circle given the angle subtended by the chord at the center of the circle.

The formula is: ( \text{Chord length} = 2 \times \text{radius} \times \sin\left(\frac{\text{central angle}}{2}\right) )

First, determine the radius of the circle using the formula for the area of a circle: ( \text{Area} = \pi \times \text{radius}^2 )

Once the radius is found, substitute it along with the given central angle (from ( \frac{11\pi}{6} ) to ( \frac{7\pi}{4} )) into the chord length formula.

After calculating, you will find the length of the chord.

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

- A triangle has corners at #(9 , 2 )#, #(4 ,7 )#, and #(5 ,8 )#. What is the radius of the triangle's inscribed circle?
- A circle C has equation #x^2+y^2-6x+8y-75=0#, and a second circle has a centre at #(15,12)# and radius 10. What are the coordinates of the point where they touch?
- What is the equation of the circle with a center at #(-4 ,6 )# and a radius of #3 #?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/6 #, and the triangle's area is #9 #. What is the area of the triangle's incircle?
- A triangle has corners at #(5 , 2 )#, #(2 ,3 )#, and #(3 ,4 )#. What is the radius of the triangle's inscribed circle?

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