1. Sec. 12.2b Apply Properties of Chords p. 771
Objective: To use relationships of arcs and chords in a circle.
Vocabulary: Review chord, arc, semicircle

3. Use congruent chords to find an arc measure.
Find mFG.
mFG = mJK = 80o.

4. If mAB = 110°, find mBC.
mBC = 110°

5. If mABC = 150°, find mAB
mAB = 75°

6. Applying Congruent Angles, Arcs, and Chords
TV  WS. Find mWS.
9n – 11 = 7n + 11
2n = 22
n = 11
mWS = 7(11) + 11
= 88°

7. Applying Congruent Angles, Arcs, and Chords
C  J, and mGCD  mNJM. Find NM.
GD  NM
GD  NM
14t – 26 = 5t + 1
9t = 27
t = 3
NM = 5(3) + 1
= 16

8. PT bisects RPS. Find RT.
RPT  SPT
mRT  mTS
RT = TS
6x = 20 – 4x
10x = 20
x = 2
RT = 6(2)
RT = 12

9. Find each measure.
A  B, and CD  EF. Find mCD.
mCD = mEF
25y = 30y – 20
20 = 5y
4 = y
CD = 25(4)
mCD = 100

11. Use a diameter. Find the length of AC.
Diameter BD is perpendicular to AC . So, by Theorem 10.5, BD bisects AC , and CF = AF. Therefore, AC = 2( AF )= 2(7) = 14.

12. CD DE CE
9x = 80 – x, so mCD = 72°
mDE = 72°
mCE = 72° + 72° = 144°

13. In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center, that is QR  ST if and only if UC = CV.

14. Find CU.
Chords QR and ST are congruent, so by Theorem 10.6 they are equidistant from C. Therefore, CU = CV.
CU = CV
2x = 5x – 9
x = 3
So, CU = 2x = 2(3) = 6.

15. Find the radius of circle C.
Find the given length. QR QU
QR = 32
QU = 16
Find the radius of circle C.
The radius of circle C = 20.

16. Using Radii and Chords Find NP. Step 1 Draw radius RN. RN = 17
Step 2 Use the Pythagorean Theorem.
SN2 + RS2 = RN2
SN = 172
SN2 = 225
SN = 15
Step 3 Find NP.
NP = 2(15) = 30

17. Find QR to the nearest tenth.
Step 1 Draw radius PQ.
PQ = 20
Step 2 Use the Pythagorean Theorem.
TQ2 + PT2 = PQ2
TQ = 202
TQ2 = 300
TQ  17.3
Step 3 Find QR.
QR = 2(17.3) = 34.6

18. T  U, and AC = 47.2. Find PL to the nearest tenth.
Find the length of PM. Find the length of UM.
Use the Pythagorean Theorem to find PU.
Subtract to find PL. PL = 12.9

19. Find each measure.
NGH
139 HL 21