Question

line segment st is congruent to which line segment?
○ \\(overline{sk}\\)
○ \\(overline{ku}\\)
○ \\(overline{ut}\\)
○ \\(overline{tk}\\)

Explanation:

In a circle, if two tangent segments are drawn from the same external point to the circle, they are congruent. Here, point \( T \) is an external point, and \( \overline{ST} \) and \( \overline{UT} \) are both tangent segments from \( T \) to the circle with center \( K \). So, by the Tangent - Segment Congruence Theorem, \( \overline{ST}\cong\overline{UT} \). The other options: \( \overline{SK} \) is a radius, \( \overline{KU} \) is a radius, and \( \overline{TK} \) is a line from the external point to the center, none of which are congruent to \( \overline{ST} \) by the tangent - segment property.

Answer:

\(\overline{UT}\)