The Euler line of a triangle contains a triangle's orthocenter, centroid, and circumcenter.
The orthocenter is where the altitudes of the triangle intersect at a single point.
The centroid is where the medians of the triangle intersect at a single point.
The circumcenter is where the perpendicular bisectors of each side of the triangle intersect at a single point.

1) What happens to the points on Euler's line if the triangle is equilateral? isosceles? scalene?
2) What happens to the points on Euler's line if the triangle is right? obtuse? acute?
3) What conditions must be met in order for the circumcenter and orthocenter to lie inside of the triangle?