Geometry Honors Section 9.1

Segments and Arcs of Circles

A *circle is a set of points, in a plane, that are equidistant from a given point.

This given point is called the

A circle can be named by using the symbol _____ and naming the center of the circle. The circle to the right is __________.

A *radius (plural: radii) is a segment from the center to a point on the circle.

MH

,

CH

,

HI

A *chord is a segment whose endpoints are on the circle.

MC

,

SE

A *diameter is a chord which contains the center of the circle.

MC

An arc is an unbroken part of a circle.

Any two distinct points on a circle divide the circle into two arcs.

The two points are called the

If the two points are the endpoints of a diameter, then each of the two A semicircle is named by its two endpoints and another point that lies on the arc.

Example: Name two semicircles.

_____ & _____

If the two points are not the endpoints of a diameter, then a minor arc and a major arc are formed.

A *minor arc is an arc which is shorter than a semicircle.

A minor arc is named by its two endpoints.

Example: Name two minor arcs.

_____ & _____

A *major arc is an arc which is longer than a semicircle. .

A major arc is named by its two endpoints and another point that lies on the arc.

Example: Name two major arcs.

_______ & _______

A *central angle of a circle is an angle whose vertex is at the center and whose sides are radii.

The arc between the outer endpoints of the two radii is arc of the central angle.

The degree measure of a minor arc is equal to the measure of its central angle. The degree measure of a major arc is equal to 360⁰ - the measure of the associated minor arc.

The degree measure of a semicircle is

When referring to the measure of an arc, use the notation __________

mHR

 100

mHN



mHRN

 170 190

mHRT

 322 100⁰ 38⁰ 132 0

The following theorem mentions congruent circles. Two circles are congruent iff their radii are congruent.

Chords and Arcs Theorem

In a circle (or in congruent circles), two chords are congruent iff the minor arcs they determine are congruent.

360  2 ( 153 )  54

Radius and Chord Theorem

If a radius is perpendicular to a chord, then the radius bisects the chord and its arc.

21 .

3 35 .

5 21 .

3 2 

b

2  35 .

5 2

b

 28 .

4

ER

 56 .

8

5 2  12 2 

c

2

c

 13