Goal 1: To use congruent chords, arcs, and central angles Goal 2: To recognize properties of lines through the center of a circle Check Skills You’ll Need.

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Presentation transcript:

Goal 1: To use congruent chords, arcs, and central angles Goal 2: To recognize properties of lines through the center of a circle Check Skills You’ll Need Find the value of each variable. If your answer is not an integer, leave it in simplest radical form. 2.2.

Solutions 1. 2.

A segment whose endpoints are on a circle is called a chord. The diagram shows the related chord and arc, and.

A central angle of a circle is an angle whose vertex is the center of the circle. <CPA is a central angle.

Theorem Within a circle or in congruent circles (1)Congruent central angles have congruent chords. (2) Congruent chords have congruent arcs. (3) Congruent arcs have congruent central angles.

Theorem Within a circle or in congruent circles (1)Chords equidistant from the center are congruent. (2) Congruent chords are equidistant from the center.

Theorems (1)In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs. (2) In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord. (3) In a circle, the perpendicular bisector of a chord contains the center of the circle. contains the center of circle T

Assignment Assignment: pp #1-19