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11.2: Chords and Arcs

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

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  1. 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

  2. Definition: CHORD Segment whose endpoints are on a circle

  3. 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

  4. Congruent central angles Congruent chords Congruent arcs

  5. ( B ( ( If , then If then ( A D C

  6. The circles are congruent. What can you conclude?

  7. THEOREM: Within a circle or in congruent circles: • Chords equidistant from the center are congruent • Congruent chords are equidistant from the center

  8. Picture pages… Each chord is the same distance to the center.

  9. Find x. x 12

  10. Find x. 24 x 8 12 12

  11. THEOREM In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs

  12. THEOREM In a circle, a diameter that bisects a chord is perpendicular to the chord.

  13. THEOREM In a circle, the perpendicular bisector of a chord contains the center of the circle.

  14. Useful relationship:

  15. 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

  16. Find x. x 3 8

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