BY THE COFFEE CUPZ

12.2 Arcs and Chords

OBJECTIVES

Apply properties of Arcs

Apply properties of Chords.

VOCABULARY

Central Angle- An angle whose vertex is the center of the circle.

Arc- An unbroken part of the circle consisting of two points called the endpoints and all the points on the circle between them.

Adjacent Arcs- Arcs of the same circle that intersect at exactly one point.

Congruent Arcs- Two arcs that have same measure.

ARCS AND THEIR MEASURESMinor arc- arc whose points are on or in the interior of a central angle.

Major Arc- An arc whose points are on or in the exterior of a central angle.

The Red line represents the minor arc, and the Black line represents the major arc.

Semicircle- when the points of the arc lie on the diameter.

ARC ADDITION POSTULATE

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

If the measure of the arc on AB is 93 degrees and the arc on CB is 40 degrees then the full arc is 133 degrees.

THEOREM 12-2-2

In a circle or congruent circles: 1. congruent central angles have congruent

chords 2. congruent chords have congruent arcs 3. congruent arcs have congruent central

angles.

APPLYING CONGRUENT ANGLES, ARCS, AND CHORDS

Find the measure of the arc of CD. The measure of the chord CD= 3x and the chord AB= 2x+27.

APPLYING CONGRUENT ANGLES, ARCS, AND CHORDS CONT.

Arc RS is congruent to Arc AB, so the central angles are congruent. Angle Y= 5y+5 and angle X= 7y- 43.

THEOREM 12-2-3

In a circle, if a radius ( or diameter) is perpendicular to a chord then it bisects the chord and its arc.

Line AB bisects line DC and Arc DC.

THEOREM 12-2-4

In a circle, the perpendicular bisector of a chord is a radius (or diameter).

AB is a diameter of Point O.

USING RADII AND CHORDS EXAMPLES

BF= 2, and FO= 3

USING RADII AND CHORDS EXAMPLES CONT.

BF= 10, and FO= 10

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