Oh, dude, the orthocenter of a triangle got its name because it's where the altitudes of the triangle intersect. It's like the center of gravity for altitudes, you know? So, "ortho" means perpendicular in Greek, and since the altitudes are perpendicular to the sides of the triangle, they just called it the orthocenter. Cool, right?
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Well, honey, the orthocenter got its name because it's the center of orthocentricity in a triangle. In simpler terms, it's where the three altitudes of the triangle intersect. So, it's called the orthocenter because it's the boss of the altitudes in that triangle.
``Orthocentre'' was invented by two mathematicians, Besant and Ferrers, in 1865, while out for a walk along the Trumpington Road, a road leading out of Cambridge toward London. In those days it was a tree-lined quiet road with a sidewalk, a favourite place for a conversational walk."
From Mathematical Gazette, Feb 1962, pp 51
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.
orthocenter
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 ...
A Triangle's OrthocenterNo, it can be outside the triangle.
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the sides of the triangle.