The orthocenter of a triangle is the point where the altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side.
In any triangle, there are three altitudes, one from each vertex. The three altitudes intersect at a single point, which is called the orthocenter. The position of the orthocenter can vary depending on the shape and size of the triangle.
Some properties of the orthocenter of a triangle include:
The orthocenter is inside the triangle if and only if the triangle is acute (i.e., all three angles are less than 90 degrees).
The orthocenter is outside the triangle if and only if the triangle is obtuse (i.e., one angle is greater than 90 degrees).
The orthocentre is located on the triangle if and only if the triangle is a right triangle (i.e., one angle is exactly 90 degrees).
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