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

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

If mAB = 110°, find mBC. mBC = 110°

If mABC = 150°, find mAB mAB = 75°

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

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

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

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

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.

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

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.

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.

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.

Using Radii and Chords Find NP. Step 1 Draw radius RN. RN = 17 Step 2 Use the Pythagorean Theorem. SN2 + RS2 = RN2 SN2 + 82 = 172 SN2 = 225 SN = 15 Step 3 Find NP. NP = 2(15) = 30

Find QR to the nearest tenth. Step 1 Draw radius PQ. PQ = 20 Step 2 Use the Pythagorean Theorem. TQ2 + PT2 = PQ2 TQ2 + 102 = 202 TQ2 = 300 TQ  17.3 Step 3 Find QR. QR = 2(17.3) = 34.6

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

Find each measure. NGH 139 HL 21