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circumcenter
Perpendicular bisectors
Locations: Acute(inside), obtuse(outside), right(midpoint of hypotenuse)
Equidistant from vertices

Incenter
Angle bisectors
Always inside
Equidistant from sides

Centroid
medians
Always inside
2/3 from vertex
(x1+x2+x3 / 3, y1+y2+y3 / 3)

orthocenter
alititudes
Locations: acute(inside), obtuse(outside), right(vertex of right angle)