Orthocenters, Medians, Incenters, Circumcenters

Circumcenter

where 3 perpendicular bisector meet

Where is the circumcenter in an acute triangle?

inside the acute triangle

Where is the circumcenter in an obtuse triangle?

outside the obtuse triangle

Where is the circumcenter in an right triangle?

on the hypotenuse of the right triangle

Centroid

where 3 medians intersect

Where is the centroid located?

Always inside the triangle

Incenter

where 3 angle bisectors intersect

Where is the incenter located?

inside all triangles

Other information about incenter

equidistant from 3 sides

Other information about circumcenter

is equidistant from 3 vertices of a triangle

Other information about centroid

2/3 of the way from the vertex to midpoint

Orthocenter

point of intersection of 3 altitudes

Where is the orthocenter of a right triangle?

On the vertex of the right angle

Where is the orthocenter of an obtuse triangle?

outside the triangle

Where is the orthocenter in an acute triangle?

inside the triangle