When a segment is tangent to a circle at a point, it means that the segment touches the circle at that point and is perpendicular to the radius that extends from the center of the circle to the point of tangency.
The relationship between the tangent and secant line segments can be described using the "Tangent-Secant Theorem." This theorem states that if a tangent segment and a secant segment are drawn from the same external point to a circle, then the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and the external part of the secant segment.
Mathematically, this can be expressed as:
\[TP^2 = TS \times TE\]
Where:
- \(TP\) is the length of the tangent segment.
- \(TS\) is the length of the secant segment.
- \(TE\) is the external part of the secant segment.
In this equation, \(TS\) is the entire secant line segment, while \(TE\) represents the part of the secant line segment that is outside the circle.
This relationship helps relate the lengths of the tangent and secant line segments when they originate from the same external point and intersect the circle.