No, it can be 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.
It must be acute angled.
Inside: acute angled triangleOn: right angled triangle Outside: obtuse angled triangle.
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 ...
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the sides of the triangle.