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

CHORD: A segment whose endpoints are on a circle

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

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

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

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

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

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

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

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

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

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

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.

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