Step 1: Recall the definition of the circumcenter.

DEFINITION: The circumcenter is the point where the perpendicular bisector of the triangle's sides converge.

Step 2: Draw the bisector to one of the triangle sides.

NOTE: Construction of the perpendicular bisector

Skill 1: Place the compass at one end of line segment.

Skill 2: Adjust the compass to slightly longer than half the line segment

length

Skill 3: Draw arcs above and below the line.

Skill 4: Keeping the same compass width, draw arcs from other end of line.

Skill 5: Place ruler where the arcs cross, and draw the line segment.

Step 3: In the same way construct bisectors to remaining triangle sides.

Step 4: Conclude that the point where these two perpendiculars intersect is the triangle's circumcenter, the center of the circle we desire.

NOTE: This point may lie outside the triangle.

Step 5: Verify that circumcenter by place the compasses' point on the intersection of the perpendiculars and set the compasses' width to one of the vertex. Draw a circle.

NOTE: The circle drawn is the triangle's circumcircle, the only circle that will

pass through all three of its vertices.