What theorem states that tangents from the same point are of equal length?

The theorem that states that tangents drawn from the same external point to a circle are of equal length is indeed the Alternate Segment Theorem. This theorem applies to circles and involves the relationship between tangents and chords. When two tangents are drawn from a single point outside the circle to touch the circle at two distinct points, the lengths of these tangents will be the same.

This property arises from the fact that both tangents create congruent right triangles formed with the radius of the circle, illustrating that both segments of the tangent line are equal in length. Understanding this theorem helps in solving problems related to circles, especially where tangents and angles formed between tangents and chords are involved.

The other options do not relate to the properties of tangents in circles. The Pythagorean Theorem concerns relationships within right triangles, the Angle Bisector Theorem deals with relations in angles within triangles, and the Triangle Inequality Theorem pertains to the lengths of sides of a triangle. Therefore, the Alternate Segment Theorem is distinctly suited to the case of tangents from a single point connecting with a circle.