# 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.

A line segment with both end points on a circle is a chord.

A chord passing though the center of a circle is a diameter.

A diameter can be viewed as two radii, and hence a diameter’s length is twice that of a radius.

A line passing through two points on a circle is a secant.

A piece of the circumference is an arc.

The area bounded by the circumference and an angle with vertex at the center of the circle is a 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 πr2, and its circumference (perimeter) is 2πr, 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 ?
 A.   π/3  B.   2π/3  C.   π  D.   4π/3  E.    7π/3

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).