Euler Line

This is a construction of the Euler Line, where G is the centroid and K is the circumcenter of the triangle. Points A', B', and C' are the midpoints of the sides of the triangle. Drag points A, B, and C.
Answer the questions below.

1. For what type of triangle will H, the orthocenter, coincide with one of the vertices of the triangle? Where is K in this type of triangle?
2. For what type of triangle will G and K coincide? (For this type of triangle, no Euler line exists.)

Veronica Robinson, Created with GeoGebra