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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