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Q: What are the properties the orthocenter of a triangle?

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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.

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

The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It may lie inside, outside, or on the triangle depending on the type of triangle. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is at the vertex opposite the right angle; and in an obtuse triangle, it is outside the triangle.

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You find the orthocenter by constructing the altitudes from the vertices in a triangle. If the triangle is obtuse, the orthocenter will fall outside the triangle. If the triangle is acute, the orthocenter will fall on the inside of the triangle. If the triangle is a right triangle, the orthocenter will lie on a vertix.

An orthocenter on an obtuse triangle actually lies outside of the triangle. In an acute triangle, the orthocenter lies within the triangle.

The orthocenter is the point where the altitudes of a triangle intersect. An orthocenter lies outside of a triangle only when the triangle is obtuse. If a triangle is acute, the orthocenter lies inside of the triangle.

If a triangle is obtuse, the orthocenter of the triangle actually lies outside of the triangle. If the triangle is acute, the orthocenter of the triangle lies on the inside of the triangle

The orthocenter of a triangle is found at the intersection of the three altitudes of the triangle. Obtuse triangles contain altitudes which are found outside of the triangle, meaning their orthocenter must be outside of the triangle as well.

On an obtuse triangle the orthocenter is located on the outside of the triangle and the orthocenter of the right triangle is located at the vertex of the triangle ...

Actually, the orthocenter of a triangle is the point where the three altitudes of the triangle intersect. The altitudes are perpendicular lines drawn from each vertex to the opposite side. The angle bisectors of a triangle intersect at the incenter, not the orthocenter.

A Triangle's OrthocenterNo, it can be outside the triangle.

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

The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It may lie inside, outside, or on the triangle depending on the type of triangle. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is at the vertex opposite the right angle; and in an obtuse triangle, it is outside the triangle.