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The relationship between the length of a tangent and a secant in a circle can be described using the tangent-secant theorem. According to this theorem, if a tangent segment is drawn from a point outside the circle to a point of tangency, and a secant segment is drawn from the same external point to intersect the circle at two points, then the square of the length of the tangent segment equals the product of the lengths of the entire secant segment and its external segment. Mathematically, if ( T ) is the length of the tangent and ( S ) is the length of the secant, the relationship can be expressed as ( T^2 = S \cdot (S - P) ), where ( P ) is the length of the part of the secant inside the circle.

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