Sec 12 2 b Apply Properties of Chords
Sec. 12. 2 b 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 m. FG = m. JK = 80 o.
If m. AB = 110°, find m. BC = 110°
If m. ABC = 150°, find m. AB = 75°
Applying Congruent Angles, Arcs, and Chords TV WS. Find m. WS. 9 n – 11 = 7 n + 11 2 n = 22 n = 11 m. WS = 7(11) + 11 = 88°
Applying Congruent Angles, Arcs, and Chords C J, and m GCD m NJM. Find NM. GD NM 14 t – 26 = 5 t + 1 9 t = 27 t=3 NM = 5(3) + 1 = 16
PT bisects RPS. Find RT. RPT SPT m. RT m. TS RT = TS 6 x = 20 – 4 x 10 x = 20 x=2 RT = 6(2) RT = 12
Find each measure. A B, and CD EF. Find m. CD = m. EF 25 y = 30 y – 20 20 = 5 y 4=y CD = 25(4) m. CD = 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 9 x = 80 – x, so m. CD = 72° m. DE = 72° m. CE = 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 2 x = 5 x – 9 x=3 So, CU = 2 x = 2(3) = 6.
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. SN 2 + RS 2 = RN 2 SN 2 + 82 = 172 SN 2 = 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. TQ 2 + PT 2 = PQ 2 TQ 2 + 102 = 202 TQ 2 = 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
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