1. The perpendicular bisector of a segment .

2. The circumcircle of a triangle .

The second construction uses the first construction twice.

Construct the perpendicular bisector of and of . The center of the circumcircle of the triangle is the intersection of these bisectors.

Perpendicular Bisector

1. Draw the line segment .

2. Draw two circles with the same radius and centers and . (Any radius works as long as the circles intersect at two points.)

3. The circles intersect at two points, and . The perpendicular bisector of is the line through these two points. The point is the midpoint of .

Circumcircle

1. Draw a triangle .

2. Draw two perpendicular bisectors of —for example, of and . Let be the intersection of the two bisectors.

3. The circumcircle has center and radius .