Chapter 11: Circles Parts of a Circle

A circle is a special type of geometric figure A circle is a special type of geometric figure. All points on a circle are the same distance from a center point.

Definition of a Circle A circle is the set of all points in a plane that are given distance from a given point in the plane, called the center of the circle. P P (Symbols) (Model) *Note that a circle is named by its center. The circle above is named circle P.

There are three kinds of segments related to circles There are three kinds of segments related to circles. A radius is a segment whose endpoints are the center of the circle and a point on the circle. A chord is a segment whose endpoints are on the circle. A diameter is a chord that contains the center.

Segments of Circles radius chord diameter R P T G P P J A PA is a radius of P. JR is a chord of K. TG is a diameter of K. *From the figures, you can note that the diameter is a special type of chord that passes through the center.

Reading Geometry The plural of radius is radii, which is pronounced RAY-dee-eye.

Suppose the radius PT of P is 5 centimeters long Suppose the radius PT of P is 5 centimeters long. So, the radius PG is also 5 centimeters. Then the diameter GT is 5 + 5 or 10 centimeters long. Notice that the diameter is twice as long as the radius. P T G R S This leads to the next two theorems.....

T R S P 11-1 G 11-2 Theorem Words Symbols All radii of a circle are congruent. PR = PG = PS = PT 11-2 The measure of the diameter d of a circle is twice the measure of the radius r of the circle. d = 2r or ½d = r

They lie in the same plane. They have the same center. Because all circles have the same shape, any two circles are similar. However, two circles are congruent if and only if their radii are congruent. Two circles are concentric if they meet the following three requirements. They lie in the same plane. They have the same center. They have radii of different lengths. R S T