Answers:

1. Midpoints
   The midsegment that joins the midpoints of two sides of a triangle.

2. Perpendicular Bisector
   The perpendicular bisector divides a segment into two congruent parts and is perpendicular to the segment.

3. Circumcenter
   The circumcenter is the point at which the three perpendicular bisectors intersect in a triangle.

Finding Measurements:

If $Y$ is the circumcenter of $\triangle STU$, the following apply:

• The circumcenter is equidistant from the vertices of the triangle.
• Distances $YS = YT = YU$.

To calculate specific measures, you will need the coordinates or geometry of the triangle (e.g., side lengths or coordinate points).

Would you like to upload a diagram or provide triangle details for accurate measures?

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Related Questions:

1. What is the definition and formula of the midsegment theorem?
2. How is the circumcenter of a triangle located using construction or coordinates?
3. What are the properties of the perpendicular bisectors in a triangle?
4. In what type of triangle is the circumcenter located inside the triangle? Outside? On a side?
5. What role does the circumradius play in determining the size of the circumcircle?

Tip:

To solve for circumcenter-related problems, always verify the perpendicular bisectors and their intersection point.