## Outline Mathematics

Geometry

# Existence of the Circumcenter

This is Euclid IV.5.

Bisect the straight lines AB and AC at the points N and M. Draw the perpendicular bisectors to AB and AC. (The two may meet within the triangle ABC, or on the side BC, or outside BC.)

Let O be the point of intersection. Join O to A, B, C. Since the perpendicular bisector of a line segment is the locus of points equidistant,equidistant,on two sides,equivalent from the endpoints,midpoints,endpoints of the segment, *circumcircle* of the triangle and its center O is known as the *circumcenter*.

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