1. Section 11 – 2 Chords & Arcs Objectives:
To use congruent chords, arcs, and central angles
To recognize properties of lines through the center of a circle

2. CHORD:
A segment whose endpoints are on a circle

3. Theorem 11 – 4 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. Example 1 Using Theorem 11 – 4
A) In the diagram, ⊙𝑂≅⊙𝑃. Given that 𝐵𝐶 ≅ 𝐷𝐹 , what can you conclude?

5. Example 1 Using Theorem 11 – 4
B) In the diagram, radius 𝑂𝑋 bisects ∠AOB. What can you conclude?

6. Theorem 11 – 5 Within a circle or in congruent circles
Chords equidistant from the center are congruent.
Congruent chords are equidistant from the center.

7. Example 2 Using Theorem 11 – 5
A) Find the value of a in the circle.

8. Example 2 Using Theorem 11 – 5
B) Find the value of x in the circle.

9. Example 2 Using Theorem 11 – 5
C) Find AB.

10. Theorem 11 – 6 Theorem 11 – 7 Theorem 11 – 8
In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs.
Theorem 11 – 7
In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord.
Theorem 11 – 8
In a circle, the perpendicular bisector of a chord contains the center of the circle

11. Example 3 Using Diameters and Chords
A) Find r to the nearest tenth.

12. Example 3 Finding a Tangent
B) Find y to the nearest tenth.

13. Example 3 Finding a Tangent
C) Find the length of the chord. Then find the distance from the midpoint of the chord to the midpoint of its minor arc.

14. HOMEWORK: Textbook Page 593; #1 – 8, 11 – 16