GeometryFormula

Chord Length Practice Problems

15 chord length problems with full worked solutions, graded from warm-up to stretch — plus an unlimited supply you can generate yourself. Every answer is computed by the same verified function that powers the chord length explorer, so the solutions cannot disagree with the formulas. Free, no account, nothing to install.

Formulas you need

  • Chord length: c=2rsin⁡ ⁣(θ2)c = 2r\sin\!\left(\dfrac{\theta}{2}\right)

where r = radius, θ = central angle (degrees), c = chord length

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Warm-up

  1. A circle of radius r = 5 has a central angle of 150°. Find the chord length (c).

    Answer & working

    9.66 units

    chord = 2r · sin(θ/2) = 2 · 5 · sin(75°) ≈ 9.66

  2. A circle of radius r = 1 has a central angle of 60°. Find the chord length (c).

    Answer & working

    1 units

    chord = 2r · sin(θ/2) = 2 · 1 · sin(30°) ≈ 1

  3. A circle of radius r = 2 has a central angle of 135°. Find the chord length (c).

    Answer & working

    3.7 units

    chord = 2r · sin(θ/2) = 2 · 2 · sin(67.5°) ≈ 3.7

  4. A circle of radius r = 2 has a central angle of 30°. Find the chord length (c).

    Answer & working

    1.04 units

    chord = 2r · sin(θ/2) = 2 · 2 · sin(15°) ≈ 1.04

  5. A circle of radius r = 1 has a central angle of 135°. Find the chord length (c).

    Answer & working

    1.85 units

    chord = 2r · sin(θ/2) = 2 · 1 · sin(67.5°) ≈ 1.85

Core practice

  1. A circle of radius r = 10 has a central angle of 120°. Find the chord length (c).

    Answer & working

    17.32 units

    chord = 2r · sin(θ/2) = 2 · 10 · sin(60°) ≈ 17.32

  2. A circle of radius r = 8 has a central angle of 90°. Find the chord length (c).

    Answer & working

    11.31 units

    chord = 2r · sin(θ/2) = 2 · 8 · sin(45°) ≈ 11.31

  3. A circle of radius r = 7 has a central angle of 60°. Find the chord length (c).

    Answer & working

    7 units

    chord = 2r · sin(θ/2) = 2 · 7 · sin(30°) ≈ 7

  4. A circle of radius r = 6 has a central angle of 150°. Find the chord length (c).

    Answer & working

    11.59 units

    chord = 2r · sin(θ/2) = 2 · 6 · sin(75°) ≈ 11.59

  5. A circle of radius r = 8 has a central angle of 135°. Find the chord length (c).

    Answer & working

    14.78 units

    chord = 2r · sin(θ/2) = 2 · 8 · sin(67.5°) ≈ 14.78

Stretch

  1. A circle of radius r = 8.5 has a central angle of 150°. Find the chord length (c).

    Answer & working

    16.42 units

    chord = 2r · sin(θ/2) = 2 · 8.5 · sin(75°) ≈ 16.42

  2. A circle of radius r = 7.5 has a central angle of 120°. Find the chord length (c).

    Answer & working

    12.99 units

    chord = 2r · sin(θ/2) = 2 · 7.5 · sin(60°) ≈ 12.99

  3. A circle of radius r = 1.5 has a central angle of 90°. Find the chord length (c).

    Answer & working

    2.12 units

    chord = 2r · sin(θ/2) = 2 · 1.5 · sin(45°) ≈ 2.12

  4. A circle of radius r = 8.5 has a central angle of 180°. Find the chord length (c).

    Answer & working

    17 units

    chord = 2r · sin(θ/2) = 2 · 8.5 · sin(90°) = 17

  5. A circle of radius r = 3.5 has a central angle of 45°. Find the chord length (c).

    Answer & working

    2.68 units

    chord = 2r · sin(θ/2) = 2 · 3.5 · sin(22.5°) ≈ 2.68

Answers are recomputed from the verified chord length function every time this page is built, and every printed line is checked to evaluate correctly. Content last reviewed August 2026. Found a mistake? Tell us — we correct and republish.

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