1. Lesson 10-3: Arcs and Chords

2. Lesson 10-3: Arcs and Chords
Theorem #1:
In a circle, if two chords are congruent then their corresponding minor arcs are congruent. E A B C D
If AB ≅ CD, then AB ≅ CD
Example:
Given mAB = 127°, find the mCD
Since the mAB = mCD
mCD = 127°
Lesson 10-3: Arcs and Chords

3. Lesson 10-3: Arcs and Chords
Theorem #2:
In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. E D A C B
If DC  AB, then DC bisects AB and AB. Therefore AE ≅ BE and AC ≅ BC
Example:
If AB = 5 cm, find AE
If mAB = 120°, find mAC
Lesson 10-3: Arcs and Chords

4. Lesson 10-3: Arcs and Chords
Theorem #3:
In a circle, two chords are congruent if and only if they are equidistant from the center. O A B C D F E
Example:
If AB = 5 cm, find CD.
Since AB = CD, CD = 5 cm.
Lesson 10-3: Arcs and Chords

5. Lesson 10-3: Arcs and Chords
Try Some Sketches:
Draw a circle with a chord that is 15 cm long and 8 cm from the center of the circle.
Draw a radius so that it forms a right triangle.
How could you find the length of the radius?
Solution:
∆ODB is a right triangle and
8cm
15cm O A B D x
Lesson 10-3: Arcs and Chords

6. Lesson 10-3: Arcs and Chords
Try Some Sketches:
Draw a circle with a diameter that is 20 cm long.
Draw another chord (parallel to the diameter) that is 14cm long.
Find the distance from the smaller chord to the center of the circle.
Solution:
10 cm
20cm O A B D C
∆EOB is a right triangle.
OB (radius) = 10 cm
14 cm E x
7.1 cm
Lesson 10-3: Arcs and Chords