Given circle \( O \) inscribed in triangle \( S T U \) with \( \overline{S Q T}, \overline{T R U} \), and \( \overline{U P S} \) tangent to \( O \) at points \( Q, R \), and \( P \) respectively. Identify a segment that is congruent to \( \overline{Q T} \).

In triangle \( S T U \), the segments that are tangent to the incircle at points \( Q, R, \) and \( P \) denote segments formed from the vertices to the points of tangency. Notably, the length of the tangent segments from each vertex to the points of tangency with the incircle is equal. Specifically, \( \overline{S Q} \) is congruent to \( \overline{S P} \) and \( \overline{T Q} \) is congruent to \( \overline{T R} \). Thus, the segment that is congruent to \( \overline{Q T} \) is \( \overline{R T} \). This congruence arises from the properties of tangents drawn from a point outside a circle, ensuring that the segments from a vertex to the points where the incircle touches the sides of the triangle are equal in length.