How Do You Find the Circumcenter of a Triangle?

For any triangle, a perfect circle can be drawn whose outside edge lies along all three points. The center of that circle is called the circumcenter of the triangle, and it can be found where the perpendicular bisectors of the triangle's sides intersect. You need a protractor, a straight-edge and a compass to find the circumcenter.

  1. Draw your triangle on grid paper

    If you were given coordinates for your triangle, mark those on a grid and draw lines between the points. If you were given a combination of lines and/or angles, draw the triangle using a compass to find the intersections of known line lengths with unknown angles of intersection.

  2. Find the bisecting points

    To bisect a line segment, find its halfway point. Divide the length of the line segment by two and measure that distance. Mark the point. Do this for all three sides.

  3. Draw perpendicular lines

    A perpendicular line forms a right angle. Use the 90-degree mark on your protractor to find the trajectory of the perpendicular lines, each starting from a bisecting point. Make a light mark at 90 degrees to guide your bisecting lines. Draw the lines using a straight-edge tool. The point at which they intersect is the circumcenter. It can be inside or outside of the triangle. To check your answer, see that the circumcenter is an equal distance between each of the triangle's points.