# Circles

A circle is a set of points in a plane equidistant from a fixed point (the center of the circle). The perimeter of a circle is called the*circumference*.

A line segment from a circle to its center is a

*radius*.

*chord*.

*diameter*.

*secant*.

*arc*.

*sector*.

A tangent line to a circle intersects the circle at only one point. The radius of the circle is perpendicular to the tangent line at the point of tangency:

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Two tangents to a circle from a common exterior point of the circle are congruent:

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*AB*â‰…

*AC*

An angle inscribed in a semicircle is a right angle:

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A central angle has by definition the same measure as its intercepted arc:

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An inscribed angle has one-half the measure of its intercepted arc:

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The area of a circle is

*Ï€r*

^{2}, and its circumference (perimeter) is 2

*Ï€r*, where

*r*is the radius:

On the test,

*Ï€*â‰ˆ 3 is a sufficient approximation for*Ï€*. You donâ€™t need*Ï€*â‰ˆ 3.14.Example

*In the figure, the circle has center O and its radius is 2. What is the length of arc ACB?*

*Ï€/3**2Ï€/3**Ï€**4Ï€/3**7**Ï€/3*

Solution

The circumference of the circle is 2Ï€*r* = 2Ï€(2) = 4Ï€.

A central angle has by definition the same degree measure as its intercepted arc.

Hence, arc *ACB* is also 60Ëš.

Now, the circumference of the circle has 360Ëš.

So arc *ACB* is (= 60/360) of the circleâ€™s circumference.

Hence, arc *ACB* = .

The answer is (B).