# A chord with a length of #4 # runs from #pi/8 # to #pi/6 # radians on a circle. What is the area of the circle?

The chord and two radii, each drawn from the center to its respective end of the chord form an isosceles triangle.

Use the Law of Cosines

The area of a circle is:

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The area of the circle can be found using the formula:

Area = π * r^2

where r is the radius of the circle.

To find the radius, we can use trigonometry. Since the chord subtends an angle of π/6 - π/8 = π/24 radians at the center of the circle, we can use the law of cosines to find the radius:

r^2 = (chord length)^2 / (2 - 2 * cos(π/24))

Given that the chord length is 4 units:

r^2 = 4^2 / (2 - 2 * cos(π/24))

Once we find the value of r, we can substitute it into the formula for the area of the circle to find the area.

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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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