ARCS AND CHORDS. A.105 B.114 C.118 D.124 A.35 B.55 C.66 D.72.

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Presentation transcript:

ARCS AND CHORDS

A.105 B.114 C.118 D.124

A.35 B.55 C.66 D.72

A.125 B.130 C.135 D.140

A.160 B.150 C.140 D.130

A.180 B.190 C.200 D.210

A ft B.165 ft C ft D ft Dianne runs around a circular track that has a radius of 55 feet. After running three quarters of the distance around the track, how far has she run?

Use Congruent Chords to Find Arc Measure Jewelry A circular piece of jade is hung from a chain by two wires around the stone. JM  KL and = 90. Find.

Use Congruent Chords to Find Arc Measure

A.42.5 B.85 C D.170

Use Congruent Arcs to Find Chord Lengths

WX= YZDefinition of congruent segments 7x – 2= 5x + 6Substitution 7x= 5x + 8Add 2 to each side. 2x= 8Subtract 5x from each side. x= 4Divide each side by 2. So, WX = 7x – 2 = 7(4) – 2 or 26. Answer:

Use Congruent Arcs to Find Chord Lengths WX= YZDefinition of congruent segments 7x – 2= 5x + 6Substitution 7x= 5x + 8Add 2 to each side. 2x= 8Subtract 5x from each side. x= 4Divide each side by 2. So, WX = 7x – 2 = 7(4) – 2 or 26. Answer: WX = 26

A.6 B.8 C.9 D.13

Use a Radius Perpendicular to a Chord Answer:

A.14 B.80 C.160 D.180

Use a Diameter Perpendicular to a Chord CERAMIC TILE In the ceramic stepping stone below, diameter AB is 18 inches long and chord EF is 8 inches long. Find CD.

Use a Diameter Perpendicular to a Chord Step 1Draw radius CE. This forms right ΔCDE.

Use a Diameter Perpendicular to a Chord Step 2Find CE and DE. Since AB = 18 inches, CB = 9 inches. All radii of a circle are congruent, so CE = 9 inches. Since diameter AB is perpendicular to EF, AB bisects chord EF by Theorem So, DE = (8) or 4 inches. __ 1 2

Use a Diameter Perpendicular to a Chord Step 3Use the Pythagorean Theorem to find CD. CD 2 + DE 2 = CE 2 Pythagorean Theorem CD = 9 2 Substitution CD = 81Simplify. CD 2 = 65Subtract 16 from each side. Take the positive square root. Answer:

Use a Diameter Perpendicular to a Chord Step 3Use the Pythagorean Theorem to find CD. CD 2 + DE 2 = CE 2 Pythagorean Theorem CD = 9 2 Substitution CD = 81Simplify. CD 2 = 65Subtract 16 from each side. Take the positive square root. Answer:

A.3.87 B.4.25 C.4.90 D.5.32 In the circle below, diameter QS is 14 inches long and chord RT is 10 inches long. Find VU.

Chords Equidistant from Center Since chords EF and GH are congruent, they are equidistant from P. So, PQ = PR.

Chords Equidistant from Center PQ= PR 4x – 3= 2x + 3Substitution x= 3Simplify. So, PQ = 4(3) – 3 or 9 Answer: PQ = 9

A.7 B.10 C.13 D.15