In a right triangle, the circumcenter is located at the midpoint of the hypotenuse.

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The main idea is that the circumcenter is the center of the circle that passes through all three vertices, so it must be equidistant from A, B, and C. In a right triangle, the hypotenuse acts as a diameter of that circumcircle. The midpoint of the hypotenuse is exactly the center of a circle with the hypotenuse as diameter. By Thales’ theorem, the right-angle vertex lies on this circle, so all three vertices lie on it. Hence the center of that circle—and thus the circumcenter—is the midpoint of the hypotenuse. This spot lies on the side of the triangle (not inside), so the circumcenter is at the midpoint of the hypotenuse.