1. 10.3 Warmup
Find the value of x given that C is the center of the circle and that the circle has a diameter of 12.
November 24, 2018
Geometry 10.3 Using Chords

2. 10.3 Warmup Factor Completely 𝟓 𝒙 𝟐 −𝟑𝟓𝒙 2. 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔
𝟓 𝒙 𝟐 −𝟑𝟓𝒙 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔
𝒙 𝟐 +𝟏𝟏𝒙+𝟐𝟒 𝒙 𝟐 −𝟔𝒙+𝟗
5. 𝒙 𝟐 −𝟒𝒙−𝟓 𝒙 𝟐 −𝟗
November 24, 2018
Geometry 10.3 Using Chords

3. 10.3 Warmup (Answers) Factor Completely 𝟓 𝒙 𝟐 −𝟑𝟓𝒙 2. 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔
𝟓 𝒙 𝟐 −𝟑𝟓𝒙 𝟔 𝒙 𝟐 +𝟏𝟐𝒙+𝟔
𝒙 𝟐 +𝟏𝟏𝒙+𝟐𝟒 𝒙 𝟐 −𝟔𝒙+𝟗
5. 𝒙 𝟐 −𝟒𝒙−𝟓 𝒙 𝟐 −𝟗
5𝑥(𝑥−7
6(𝑥+1)(𝑥+1
𝑥+8)(𝑥+3
𝑥−3)(𝑥−3
𝑥−5)(𝑥+1
𝑥−3)(𝑥+3
November 24, 2018
Geometry 10.3 Using Chords

4. Geometry
10.3 Using Chords

5. 10.3 Essential Question
In a circle, what is true when a radius is perpendicular to a chord?
November 24, 2018
Geometry 10.3 Using Chords

6. Goals Compute arc measures and angle measures November 24, 2018
Geometry 10.3 Using Chords

7. Arc Theorems
November 24, 2018
Geometry 10.3 Using Chords

8. Congruent Corresponding Chords Theorem (Thm 10.6)
In the same circle, or in congruent circles, two minor arcs are congruent if and only if corresponding chords are congruent.
November 24, 2018
Geometry 10.3 Using Chords

9. Theorem 10.6 B A C D
November 24, 2018
Geometry 10.3 Using Chords

10. Example 1 Solve for x. 5x + 10 = 120 5x = 110 x = 22 (5x + 10) 120
November 24, 2018
Geometry 10.3 Using Chords

11. Example 2 x 𝑥+𝑥+150=360 2𝑥+150=360 150 ͦ 2𝑥 =210 𝑥=105 x =105°
November 24, 2018
Geometry 10.3 Using Chords

12. Perpendicular Chord Bisector Theorem (Thm 10.7)
If a diameter is perpendicular to a chord, then it bisects the chord and the subtended arc.
November 24, 2018
Geometry 10.3 Using Chords

13. Example 3 Solve for x. 2x = 52 x = 26 52 2x November 24, 2018
Geometry 10.3 Using Chords

14. Example 4 𝐶𝐸=5+5=10 9𝑥=80−𝑥 10𝑥=80 𝑥=8 =2∙9 8 =144°
a. Find the length of 𝐶𝐸 . b. Find .
𝐶𝐸=5+5=10
9𝑥=80−𝑥
10𝑥=80
𝑥=8
=2∙9 8 =144°
November 24, 2018
Geometry 10.3 Using Chords

15. Perpendicular Chord Bisector Converse Theorem (Thm 10.8)
If a chord is the perpendicular bisector of another chord, then it is a diameter.
Diameter
November 24, 2018
Geometry 10.3 Using Chords

16. Equidistant Chords Theorem (Thm 10.9)
Two chords are congruent if and only if they are equidistant from the center of a circle.
November 24, 2018
Geometry 10.3 Using Chords

17. The red wires are the same length because they are the same distance from the center of the grate.
November 24, 2018
Geometry 10.3 Using Chords

18. Example 5 Solve for x. 16 4x – 2 = 16 4x = 18 x = 18/4 x = 4.5 4x – 2
November 24, 2018
Geometry 10.3 Using Chords

19. Example 6 In the diagram, QR = ST = 16, CU = 2x, and
CV = 5x − 9. Find the length of the radius of ⊙C.
November 24, 2018
Geometry 10.3 Using Chords

20. Your Turn In the diagram, JK = LM = 24, NP = 3x,
and NQ = 7x − 12. Find the radius of ⊙N.
November 24, 2018
Geometry 10.3 Using Chords

21. Summary
Congruent chords subtend congruent arcs and are equidistant from the center of the circle.
If a diameter is perpendicular to a chord, then it bisects it.
November 24, 2018
Geometry 10.3 Using Chords

22. Homework
November 24, 2018
Geometry 10.3 Using Chords