Frequently Asked Questions
What is the circumcenter?
The point equidistant from all three vertices of a triangle. It is the intersection of the three perpendicular bisectors of the sides.
Can the circumcenter be outside the triangle?
Yes, for an obtuse triangle. For an acute triangle the circumcenter is inside, and for a right triangle it lies exactly at the midpoint of the hypotenuse.
Circumcenter or incenter?
Circumcenter is equidistant from the three vertices and lies on the perpendicular bisectors. Incenter is equidistant from the three sides and lies on the angle bisectors.
How do you find the circumcenter from three coordinates?
The circumcenter is the intersection of the perpendicular bisectors of any two sides. Set up the two bisector equations from the midpoints and slopes, then solve them simultaneously; the result is equidistant from all three vertices.
What is the difference between the circumcenter and the centroid?
The circumcenter is the point equidistant from all three vertices (the center of the circumscribed circle), while the centroid is the average of the vertices (the center of mass, where the medians meet). They coincide only in an equilateral triangle.
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