Description:
Circle questions test your ability to apply the laws for the circumference
and area of a circle found at the beginning of every math section. Harder
questions involve segments of a circle and require you to apply a proportion
in order to solve them.
Approach:
Generally, if you can find the radius,
you can answer a circle question. Remember that radii form perpendicular angles
with lines drawn tangent to a circle.
1) Circle Equations
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Useful Circle Equations:
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![[Image: Diagram of a circle]](/MindFish/resized-image.ashx/__size/550x0/__key/CommunityServer.Wikis.Components.Files/sat_5F00_preparation/3250.Circle.png)
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1-1. Practice:
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What is the circumference of a circle with a radius of 14?
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A circle has a radius of 3. What is its area?
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If a circle has an area of 81π, what is its circumference?
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A circle has a circumference of 10π. What is its area?
2) Sector of a Circle
In order to solve for either the arc-length (L) or area (A) of a sector,
you can apply the following proportion:
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θ⁄360 = L
⁄2(π)r =
A⁄(π)r2
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θ = angle measure of the sector
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r = radius of the circle
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L = arc length of the sector
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A = area of the sector
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![[Image: Diagram of measuring a circle]](/MindFish/resized-image.ashx/__size/550x0/__key/CommunityServer.Wikis.Components.Files/sat_5F00_preparation/6403.GoodCircleSector.png)
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If, for example, x = 90 and r = 10:
90⁄360 = 1⁄4 =
L⁄20(π) = A⁄100(π)
Therefore: area = 5(π)
and circumference = 25(π)
2-1. Practice:
If a sector's central angle measures 60 degrees and the circle's radius is 6, what is the area of the sector? What is the sector's arc length?
