Question

In which type of triangle is the orthocenter on the perimeter of the triangle?

a right triangle
an acute triangle
an obtuse triangle
an equilateral triangle

Answer 1

Right triangle.

In a right triangle the two legs are themselves altitudes, so their intersection is the right-angle vertex — a point on the triangle's perimeter. (In an acute triangle the orthocenter is inside; in an obtuse triangle it's outside; in an equilateral it is inside.)