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Circumcenter
The point where the perpendicular bisectors of the three sides of the triangle intersect
The incenter is the point of concurrency of the perpendicular bisectors of the triangle's sides
The angle bisectors of a regular polygon are always concurrent. And the point that they meet at is also the meeting point of the perpendicular bisectors of the sides. If it is a polygon with an odd nmber of sides, the "medians" [line from vertex to mid-point of opposite side] and "altitudes" [perpendicular from vertex to opposite side] will also meet at the same point.
A right triangle. See: http://en.wikipedia.org/wiki/Circumscribed_circle#Circumscribed_circles_of_triangles
circumcenter
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Angle bisectors intersect at the incenter which is equidistant from the sides
Circumcenter. The circumcenter of a triangle is the center of the circumcircle of the triangle. It is the point, O, at which the perpendiculars bisectors of the sides of a triangle are concurrent. The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter.
The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.
The perpendicular bisectors of the sides of a triangle intersect at its circumcentre.
The bisectors of the angles of a triangle are concurrent at a point called the incentre which is also the centre of the inscribed circle that touches all three sides.
The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.
circumcenter
Circumcenter
The point where the perpendicular bisectors of the three sides of the triangle intersect
The incenter is the point of concurrency of the perpendicular bisectors of the triangle's sides