1. Warm-Up a. mBD b. mACE c. mDEB d. mABC 140° 130° 230° 270°
Find the measure of each arc of circle Z.
a. mBD
b. mACE
c. mDEB
d. mABC
140° B A
35°
130°
90° Z C
105°
75°
55°
230° E D
270°

2. Apply Properties of Chords
Section 10 – 3 & Section 10 – 6
Apply Properties of Chords

3. Theorem 10-3
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. B C D A

4. Theorem 10-4
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. T S Q P R

5. Theorem 10-5
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. T S Q P R

6. Theorem 10-6
In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. C A F G P B D

7. Theorem 10-14 Segments of Chords Theorem
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. C A E B D
EA • EB = EC • ED

8. Example 1 ~ ~ Since AB and CD are = chords, then AB = CD. ~ mCD = 108°
In circle R, AB = CD and mAB = 108°. Find mCD. A ~ C
Since AB and CD are = chords, then AB = CD. ~
108° R
mCD = 108° B D

9. Example 2
Use the diagram of Circle C to find the length of BF. Tell what theorem you used. A
10 units 10 B D F C
Theorem 10-5: If a diameter is perpendicular to a chord than the diameter bisects the chord and its arc. G

10. Example 3 Use Theorem 10-6 QR = ST 2x + 6 = 3x – 1 x = 7
In the diagram of Circle P, PV = PW, QR = 2x + 6 and ST = 3x – 1. Find QR.
Use Theorem 10-6 R
QR = ST V S
2x + 6 = 3x – 1 Q W P
x = 7 T
QR: 2(7) + 6 =
QR = 20 units

11. Example 4 Use Theorem 10-14 SV • VU = RV • VT x • 4x = (x + 1) • 3x
Find RT and SU.
Use Theorem 10-14
SV • VU = RV • VT S R x
x + 1 T V 3x
x • 4x = (x + 1) • 3x
4x2 = 3x2 + 3x 4x
x2 = 3x U
x = 3
RT = (x + 1) + 3x
SU = x + 4x
RT = (3 + 1) + 3(3)
SU = 3 + 4(3)
RT = 13
SU = 15

12. Homework Section 10-3 Page 667 – 668 (3 – 11, 15, 18 – 20)
(3, 4, 13, 16)