When Is the Circumcenter on the Triangle?

The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (i.e., the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (i.e. meeting at one point).

How do you find the circumcenter of a triangle?

To find the circumcenter of any triangle, draw the perpendicular bisectors of the sides and extend them. The point at which the perpendicular intersects each other will be the circumcenter of that triangle.

Can the circumcenter be on the triangle?

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.