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An orthocenter on an obtuse triangle actually lies outside of the triangle. In an acute triangle, the orthocenter lies within the triangle.
Construct a scalene triangle and then from each of its vertices draw a straight line that is perpendicular to its opposite side and where these 3 straight lines intersect it is the orthocenter of the triangle. The position of the orthocenter can vary depending on what type of triangle it.
An equilateral triangle perhaps depending on your meaning of 'ON the triangle'
The orthocenter may fall outside of a triangle. The orthocenter usually lies within the inside the triangle. However this is only the case if the triangle is acute.
ORTHOCENTER