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Sect. 12-3 Properties of Chords and Arcs

Sect. 12-3 Properties of Chords and Arcs. Geometry Honors. What and Why. What? Find the lengths of chords and measures of arcs of a circle. Locate the center of a circle using chords. Why? To find the radius of a circle in real-life situations such as archaeology. Congruent Arcs and Chords.

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Sect. 12-3 Properties of Chords and Arcs

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  1. Sect. 12-3Properties of Chords and Arcs Geometry Honors

  2. What and Why • What? • Find the lengths of chords and measures of arcs of a circle. • Locate the center of a circle using chords. • Why? • To find the radius of a circle in real-life situations such as archaeology.

  3. Congruent Arcs and Chords • Segments with endpoints on a circle are chords of the circle. • The diagram shows arc and its related chord • Is a diameter a chord? • Is a radius a chord?

  4. Theorem 12-5 • In the same circle or in congruent circles, • (1) congruent central angles have congruent arcs; and • (2) congruent arcs have congruent central angles.

  5. Theorem 12-6 • In the same circle or in congruent circles, • (1) congruent chords have congruent arcs • (2) congruent arcs have congruent chords

  6. Theorem 12-7 • A diameter that is perpendicular to a chord bisects the chord and its arc.

  7. Example • Chord is 24 in. long and 5 in. from the center of circle O. • Find the radius of circle O. • Find the

  8. Theorem 12-8 • The perpendicular bisector of a chord contains the center of the circle.

  9. Chords Equidistant from the Center of a Circle • Theorem 12-9 • In the same circle or in congruent circles, • (1) chords equidistant from the center are congruent • (2) congruent chords are equidistant from the center.

  10. Proof: Theorem 12-9, part (1)Given: circle O, Prove:

  11. Proof: Theorem 12-9, part (1)Given: circle O, Prove:

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