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11.2: Chords and Arcs. Objectives: Students will be able to… Use congruent chords, arcs and central angles. Recognize properties of lines through the center of a circle. Definition: CHORD. Segment whose endpoints are on a circle. THEOREM:. Within a circle or in congruent circles:
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11.2: Chords and Arcs Objectives: Students will be able to… Use congruent chords, arcs and central angles. Recognize properties of lines through the center of a circle
Definition: CHORD Segment whose endpoints are on a circle
THEOREM: Within a circle or in congruent circles: • Congruent central angles have congruent chords • Congruent chords have congruent arcs • Congruent arcs have congruent central angles
Congruent central angles Congruent chords Congruent arcs
( B ( ( If , then If then ( A D C
THEOREM: Within a circle or in congruent circles: • Chords equidistant from the center are congruent • Congruent chords are equidistant from the center
Picture pages… Each chord is the same distance to the center.
Find x. x 12
Find x. 24 x 8 12 12
THEOREM In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs
THEOREM In a circle, a diameter that bisects a chord is perpendicular to the chord.
THEOREM In a circle, the perpendicular bisector of a chord contains the center of the circle.
Example: Find x to the nearest tenth. • A diameter perpendicular to a chord bisects the chord • Since x is bisected by the segment on diameter, use pythagorean theorem to find half of x, then double answer. 6 4 x
Find x. x 3 8