Arcs and Chords – Segment Lengths in Circles Date________________ Period____ Find the length of each arc.

Arcs and Chords – Segment Lengths in Circles Date________________ Period____ Find the length of each arc. Round your answers to the nearest tenth. 1) mAB = 60°, r = 10 cm 2) mCD = 45°, d = 8 in 3) mEF = 120°, r = 6 m 4) mGH = 150°, d = 12 ft 5) mJK = 75°, r = 5.5 cm 6) mLM = 30°, d = 9 in 7) mNP = 135°, r = 7 m 8) mQR = 165°, d = 10 ft Find the length of each chord. Round your answers to the nearest tenth. 9) mAB = 60°, r = 10 cm 10) mCD = 45°, d = 8 in 11) mEF = 120°, r = 6 m 12) mGH = 150°, d = 12 ft 13) mJK = 75°, r = 5.5 cm 14) mLM = 30°, d = 9 in 15) mNP = 135°, r = 7 m 16) mQR = 165°, d = 10 ft
Kuta Software – Infinite Geometry Name___________________________________ Arcs and Chords – Segment Lengths in Circles Date________________ Period____ Find the length of each arc. Round your answers to the nearest tenth. 1) mAB = 60°, r = 10 cm 2) mCD = 45°, d = 8 in 3) mEF = 120°, r = 6 m 4) mGH = 150°, d = 12 ft 5) mJK = 75°, r = 5.5 cm 6) mLM = 30°, d = 9 in 7) mNP = 135°, r = 7 m 8) mQR = 165°, d = 10 ft Find the length of each chord. Round your answers to the nearest tenth. 9) mAB = 60°, r = 10 cm 10) mCD = 45°, d = 8 in 11) mEF = 120°, r = 6 m 12) mGH = 150°, d = 12 ft 13) mJK = 75°, r = 5.5 cm 14) mLM = 30°, d = 9 in 15) mNP = 135°, r = 7 m 16) mQR = 165°, d = 10 ft

The Correct Answer and Explanation is:

Arc Length Answers (nearest tenth)

Use the formula: Arc Length = (θ / 360) × 2πr If diameter is given, use r = d ÷ 2.

1. 10.5 cm
2. 3.1 in
3. 12.6 m
4. 15.7 ft
5. 7.2 cm
6. 2.4 in
7. 16.5 m
8. 14.4 ft

Chord Length Answers (nearest tenth)

Use the formula: Chord = 2 × r × sin(θ / 2) where θ is in degrees and r is radius.

9. 10.0 cm
10. 3.2 in
11. 10.4 m
12. 11.2 ft
13. 8.0 cm
14. 2.3 in
15. 9.9 m
16. 9.8 ft

Explanation

To find the arc length, we measure how much of the circle’s circumference the arc spans. The arc covers a proportion of the whole circle equal to its central angle divided by 360. Once we find that fraction, we multiply it by the total circumference (2πr) to find the arc length. For example, if the central angle is 60 degrees and the radius is 10 cm, the arc covers 1/6 of the circle. So the arc length is (1/6) × 2π × 10, which is approximately 10.5 cm.

For the chord length, we apply trigonometry. A chord stretches straight from one endpoint of an arc to the other. If we draw two radii to the endpoints, we form an isosceles triangle, and the chord becomes the base. By splitting the triangle in half, we use right triangle properties and sine of half the angle to determine the half-length of the chord, then double it. The formula 2 × r × sin(θ / 2) is derived from this concept.