The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle. Since every triangle is cyclic, every triangle has a circumscribed circle, or a circumcircle.

Does every triangle have a circumcenter?

Theorem: All triangles are cyclic, i.e. every triangle has a circumscribed circle or circumcircle. ... (Recall that a perpendicular bisector is a line that forms a right angle with one of the triangle's sides and intersects that side at its midpoint.) These bisectors will intersect at a point O.

Can a triangle not have circumcenter?

The circumcenter is not always inside the triangle. In fact, it can be outside the triangle, as in the case of an obtuse triangle, or it can fall at the midpoint of the hypotenuse of a right triangle. See the pictures below for examples of this.