Secants and chords

Math

Definition

A chord is a line segment with both endpoints on a circle. A secant is a line that intersects a circle at exactly two points, extending beyond the circle. Theorems about secants and chords relate the lengths of segments and the measures of intercepted arcs.

Examples

  • A diameter is the longest chord of a circle
  • Two secants drawn from the same external point: the products of their segments are equal
  • A chord 6 cm from the center of a circle with radius 10 cm has length 16 cm
Key Fact

Two chords intersecting inside a circle: (segment 1a)(segment 1b) = (segment 2a)(segment 2b)

Related Terms

Central and inscribed angles Circles and circumference Arc length and sector area Tangent lines

Study This Concept

Practice secants and chords with free review games in these units:

Geometry Unit 9: Circles