Measures of Tangent, Chords, and Secant Segments

Segments Formed by Two Intersecting Chords

Length of Inscribed Cords Theorem: If two chords intersect within a circle, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other.

Segments Formed by a Tangent Intersecting a Secant

Theorem 1: If a tangent and a secant are drawn to a circle from an external point, then the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external segment.

Theorem 2: If a tangent and a secant are drawn to a circle from an external point, then the length of the tangent segment is the mean proportional between the lengths of the secant segment and its external segment.

Theorem 3: If two secant segments are drawn to a circle from an external point, then the product of the lengths of one secant segment and its external segment is equal to the product of the lengths of the other secant segment and its external segment.

Learn more about measures of tangents, chords, and secant segments below.

Measures of Tangent, Chords, and Secant Segments

Practice: Find measures of chords, secants, and tangents in the following exercises.

Measures of Tangent, Chords, and Secant Segments 1

Measures of Tangents, Chords, and Secant Segments 2