# A circle's center is at #(5 ,4 )# and it passes through #(1 ,4 )#. What is the length of an arc covering #(5pi ) /8 # radians on the circle?

Use the distance formula, the the arc length formula.

First things first use the distance formula for two points:

which boils down to:

in this case.

This will give you the radius of the circle. Since both points are at the same height, you didn't really need the distance formula, but hey, why not be general?

Then use the arc length formula for a circle.

Where L is the arc length, r is the radius, and t is the central angle.

This gives you an arc length of:

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To find the length of an arc on a circle, you can use the formula:

Arc Length = Radius × Angle in radians

Given that the circle's center is at (5, 4) and it passes through (1, 4), the radius of the circle is the distance between the center and any point on the circle, which can be calculated using the distance formula.

Using the distance formula:

Radius = √((5 - 1)^2 + (4 - 4)^2) = √(4^2 + 0^2) = √16 = 4

Now, we can use the formula for arc length:

Arc Length = Radius × Angle in radians = 4 × (5π/8) = 5π units

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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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- Two circles have the following equations #(x -1 )^2+(y -4 )^2= 36 # and #(x -1 )^2+(y +5 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?
- A triangle has corners at #(2 , 4 )#, #(1 ,3 )#, and #(6 ,7 )#. What is the radius of the triangle's inscribed circle?
- A triangle has sides with lengths of 6, 4, and 2. What is the radius of the triangles inscribed circle?

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