Circles and Length of Segments:

Theorem:

When two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Theorem:

When two secant segments are drawn to a circle from a point outside the circle, the product of the lengths of one secant segment and its outer segment equals the product of the lengths of other secant segment and its outer segment.

Theorem:

When a secant segment and a tangent segment are drawn to a circle from a point outside the circle, the product of the length of the secant segment and its outer segment is equal to the square of the length of the tangent segment.