1. Apply Properties of Chords
Chapter 10.3
Apply Properties of Chords

2. Essential Question
What are the properties of chords?

3. What’s a chord again?
A chord is a segment inside a circle with endpoints on the circle.
Any chord will divide a circle into 2 arcs, a major and minor arc.

4. If there are any 2 chords of the same length, then their arcs are congruent.

5. What are the measures of arcs AB, AE, and BD?
360 – 75 – 75 = 210
210÷2 = 105
105º
105º

6. Find the measures of arcs AB and DB…Hint: they should be the same!
360 – 128= 232
232÷2 = 116

8. What do you know about the 2 segments?
3x + 7 = 4x
7 = x

9. Find x
5x - 6 = 2x + 9
3x - 6 = 9
3x = 15
x = 5

10. Find x
6x + 9 = 8x - 13
9 = 2x - 13
22 = 2x
11 = x

11. The chords are congruent when they are the same distant from the center.

12. What do we know about the 2 segments?
5x - 7 = 18
5x = 25
x = 5

13. If the 2 chords are congruent, what do we know about AQ and BQ?
4x + 1 = x + 8
3x + 1 = 8
3x = 7
x = 2.333

14. Find the given arc
If the diameter is perpendicular to a chord then it splits the chord in half.
Find the other 2 arcs
125°
125°
A circle is 360º, so …
360 – 55 – 55 = 250
250 ÷ 2 = 125°

15. Find the missing arcs
If there are 4 arcs of equal size, what do you divide 360 by? 4
360 ÷ 4 = 90

16. Classzone eWorkbook 10.3