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Centroid
Always inside; formed by medians; ration 2:1
Circumcenter
Acute- In
Right - On
Obtuse - Out
formed by perp. bisectors; point of concurrency is equidistant from the three verteces of a triangle
Incenter
Always inside, formed by angle bisectors, point of concurrency is equidistant from the sides of the triangles.
Orthocenter
Acute - In
Right - On
Obtuse - Out
formed by Altitudes