Which formula describes the relationship between tangent and secant segments?

The formula that accurately describes the relationship between tangent and secant segments is that the square of the length of the tangent segment is equal to the product of the external segment of the secant and the whole secant. This is expressed mathematically as:

tangent² = external segment × whole secant.

This formula is derived from the Secant-Tangent Theorem, which states that for any point outside a circle, when a tangent is drawn from that point to the circle, and a secant is drawn that intersects the circle, the relationship holds true. Here’s how this works:

• The tangent segment is the line segment from the external point to the point of tangency on the circle.

• The secant segment consists of the part from the external point to the intersection point with the circle and extends to the circle itself.

• The external segment is the length from the external point to the point where the secant intersects the circle.

• The whole secant is the entire length from the external point up to the far intersection point with the circle.

Thus, if you take the tangent segment and square its length, it will equal the product of the lengths of the external segment and the entire length of the secant. This relationship