Theorem 12-14
Intersecting Secants or tangents
Include Formula
Formula: If two secants (or tangents) intersect outside a circle, then the product of the lengths of one secant and its external segment is equal to the product of the length of the other secant and its external segment.
In other words: If two secants (or tangents) AB and AC intersect outside a circle, with points A, B, C, and D lying on the circle and segments AD and BC intersecting at point E, then:
AB * AE = AC * AD
Theorem 12: If a tangent and a secant are drawn from an external point to a circle, then the square of the length of the tangent is equal to the product of the lengths of the secant and the external segment of the secant.
Formula:
Let 'P' be the external point, 'T' be the point of tangency, 'A' be the point where the secant intersects the circle, and 'B' be the other endpoint of the secant.
The formula for Theorem 12 is given as:
PT^2 = PA * PB