Section 9.1 – Chords and Arcs

Circle – the set of all points equidistant from a given point, called the center

Radius (radii) – a segment from the center of a circle to a point on the circle

Chord – a segment whose endpoints lie on the circle

Diameter – a chord that contains the center

O is the center

is a chord

is a radius

is a diameter

D

B

Arc – an unbroken part of a circle.

Any two distinct points (endpoints) divide the circle into 2 arcs

Semicircle – an arc whose endpoints are endpoints of a diameter

Minor arc – an arc that is shorter than a semicircle

A minor arc is named by its 2 endpoints

Major arc – an arc that is longer than a semicircle

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

Central angle – an angle whose vertex is the center of the circle

A central angle is used to find the measure of arcs

Intercepted arc – an arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the central angle

Degree of semicircle = 180

Degree of minor arc = measure of its central angle

Degree of major arc = 360 – measure of minor arc

Arc length = part (fraction) of the circumference

L =

Theorem: In a circle, the arcs of congruent chords are congruent

Theorem: In a circle, the chords of congruent arcs are congruent