Secants and Intersecting Chords

When two chords cross inside a circle, or two secants meet outside, there are special rules to find missing lengths and angles.

When two chords cross inside a circle, multiply the pieces: a × b = c × d

How It Works

A chord is a line segment with both endpoints on the circle. The diameter is the longest possible chord — it goes through the center.

A secant is a line that passes through a circle, hitting it at TWO points. Think of it as a chord that keeps going past the circle.

When two chords cross inside a circle, multiply the pieces: (piece 1) × (piece 2) = (piece 3) × (piece 4). This always works!

When two secants come from the same point outside the circle, use: (whole length 1) × (outside part 1) = (whole length 2) × (outside part 2).

The angle where two chords cross = half the sum of the two arcs they cut off. Formula: angle = ½(arc1 + arc2).

Intersecting Chords (lengths)

a × b = c × d

When two chords intersect, the products of their segments are equal.

Intersecting Chords (angle)

angle = ½ × (arc₁ + arc₂)

The angle formed equals half the sum of the two intercepted arcs.

Two Secants from Outside

(whole₁) × (outside₁) = (whole₂) × (outside₂)

For two secants from the same external point, the products of whole and external segments are equal.

Secant-Tangent from Outside

(whole secant) × (outside part) = tangent²

When a secant and tangent come from the same point, the secant product equals the tangent squared.