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How to Circumscribe a Triangle

Every triangle can be circumscribed by a circle, meaning that one circle — and only one — goes through all three vertices (corners) of any triangle. In laymen’s terms, any triangle can fit into some circle with its corners touching the circle.

To circumscribe a triangle, all you need to do is find the center of the circle. You can then find the radius of the circle, because the distance from the center of the circle to any one of the triangle’s vertices is the radius. To find the center of the circle, you need to find the circumcenter of the triangle. The circumcenter is found at the intersection of the three perpendicular bisectors of the sides of the triangle. This exercise is a nice one to try your hand at with a compass and straightedge or with some of the new geometry software. You would need to find the midpoints of each side of the triangle. Then you construct lines perpendicular to each of the sides through their midpoints. These perpendiculars always intersect in one point — sometimes even outside the triangle.

A circumscribed triangle.
A circumscribed triangle.
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