Question

line segment st is congruent to which line segment?
$overline{sk}$
$overline{ku}$
$overline{ut}$
$overline{tk}$

Explanation:

From the diagram, \( \overline{KS} \) and \( \overline{KU} \) are radii of the circle, so \( \overline{KS} \cong \overline{KU} \). \( \overline{KT} \) is a common segment to triangles \( \triangle KST \) and \( \triangle KUT \). Additionally, \( \overline{ST} \) and \( \overline{UT} \) are tangent segments from point \( T \) to the circle. By the tangent segment theorem, two tangent segments from a single external point to a circle are congruent.

Answer:

\( \boldsymbol{\overline{UT}} \)