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Chord-Tangent Angle Theorem Calculator

Online chord length calculator. Enter the radius and the distance from center to chord to find the chord length by the Pythagorean theorem—ideal for circle geometry.

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r² = d² + (chord/2)²
Radius
Center-to-chord distance

📖 Tutorial | Chord Theorem

1. Definition
The diameter perpendicular to a chord bisects it and its arcs.
2. Formula & Notation
rRadius
dDistance to chord
chord2√(r²−d²)
3. Properties & Laws
  • Perpendicular diameter bisects chord;
  • r²=d²+(chord/2)²;
  • Diameter is longest;
  • Shorter distance, longer chord.
4. Steps
  1. Enter r and d;
  2. Click "Find Chord";
  3. Or click "Load Example".
5. Worked Examples
Example: r=5, d=3.
Solution: half 4, chord 8.
6. Common Pitfalls
Distance can be 0 (diameter);
d must be less than r;
Chord is twice the half.

❓ FAQ | Chord Theorem

The theorem?
Perpendicular diameter bisects chord and arcs.
Chord length?
2√(r²−d²).
r=5,d=3?
8.
Distance to chord?
Perpendicular from center.
Longest chord?
Diameter.
Diameter bisecting chord?
Perpendicular to it.