# A circle's center is at #(8 ,1 )# and it passes through #(2 ,5 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

Given :

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

To find the length of an arc covering π/6 radians on the circle, you first need to find the radius of the circle using the given points. Then, you can use the formula for the length of an arc:

Length of arc = radius * angle

Given points: Center of the circle: (8, 1) Point on the circle: (2, 5)

Using the distance formula, you can find the distance between these two points, which represents the diameter of the circle. Then, divide the diameter by 2 to find the radius.

Radius = (1/2) * √((8 - 2)^2 + (1 - 5)^2) = (1/2) * √((6)^2 + (-4)^2) = (1/2) * √(36 + 16) = (1/2) * √52 = √13

Now, you can find the length of the arc covering π/6 radians:

Length of arc = √13 * (π/6) = (π/6) * √13

So, the length of the arc covering π/6 radians on the circle is (π/6) * √13.

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 triangle has corners at #(9 ,1 )#, #(4 ,6 )#, and #(7 ,4 )#. What is the area of the triangle's circumscribed circle?
- What is the equation of the circle with a center at #(2 ,1 )# and a radius of #3 #?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/8 #, vertex B has an angle of #(pi)/12 #, and the triangle's area is #12 #. What is the area of the triangle's incircle?
- The coordinates of the endpoints of the diameter of a circle are #(3, 8)# and #(-7, 2)#. What are the coordinates of the center of the circle?
- How do you write the general form given a circle that passes through the given points. P(-2, 0), Q(1, -3), R(-2, -6)?

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