Summary
Highlights
This section introduces the theorem stating that if two chords of a circle intersect, the product of the segments of one chord equals the product of the segments of the other chord. An illustration shows chords CB and DE intersecting at point F, leading to the equation CF * FB = DF * FE. Examples are provided to calculate unknown segment lengths using this theorem.
The concept of an external secant segment is defined as the part of a secant segment that lies outside the circle. Several figures are presented, and the viewer is asked to identify the external secant segments within each illustration.
This part details theorems related to secant and tangent segments drawn from an exterior point. The first theorem states that if two secant segments are drawn from an exterior point, the product of the lengths of one secant segment and its external part is equal to the product of the lengths of the other secant segment and its external part. Examples demonstrate applying this theorem to find unknown values, including a case involving a quadratic equation.
The final theorem covered is for a tangent segment and a secant segment drawn from an exterior point. It states that the square of the length of the tangent segment is equal to the product of the length of the secant segment and its external part. Examples illustrate how to use this theorem to calculate unknown lengths, involving squaring tangent lengths and multiplying secant segment components.