# 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:

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

*AB*≅

*AC*

An angle inscribed in a semicircle is a right angle:

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

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

The area of a circle is

*πr*

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

*πr*, where

*r*is the radius:

On the test,

*π*≈ 3 is a sufficient approximation for*π*. You don’t need*π*≈ 3.14.Example

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

*π/3**2π/3**π**4π/3**7**π/3*

Solution

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

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

Hence, arc *ACB* is also 60˚.

Now, the circumference of the circle has 360˚.

So arc *ACB* is (= 60/360) of the circle’s circumference.

Hence, arc *ACB* = .

The answer is (B).