1. Unit 3: Circles & Spheres
Math 2 – 6.3
Properties of Chords

2. Theorem
In the same circle, or in congruent circles, two minor arcs are congruent if and only if …
their corresponding chords are congruent

3. Example 1:
Find the chord length.
a. b.

4. Example 2:
Find the arc length.
a. b.

5. Theorem
If one chord is a perpendicular bisector of another chord, then …
the first chord is a diameter

6. Tell whether QS is a diameter of the circle. If not, explain why.
Example 3:
Tell whether QS is a diameter of the circle. If not, explain why.
a. b.

7. Theorem If a diameter of a circle is perpendicular to a chord, then …
the diameter bisects the chord and its arc.

8. Find the measures of CB and BE.
Example 4:
Find the measures of CB and BE.

9. Find the given measures. a. b.
Example 5:
Find the given measures.
a. b.

10. Theorem
In the same circle, or in congruent circles, two chords are congruent if and only if …
they are equidistant from the center

11. Example 6:
Find EF.

12. Example 7:
Use the diagram to match the chord or arc with a congruent chord or arc.