Frequently Asked Questions
What is the orthocenter?
The point where the three altitudes of a triangle meet. The altitude from each vertex is perpendicular to the opposite side.
Can it be outside the triangle?
Yes, for an obtuse triangle. For an acute triangle the orthocenter is inside, and for a right triangle it coincides with the right-angle vertex.
What is the Euler line?
A line that contains the orthocenter H, centroid G, and circumcenter O of a triangle. The centroid divides the segment from O to H in the ratio 1:2.
How do you find the orthocenter with coordinates?
Find the equations of two altitudes, each passing through a vertex and perpendicular to the opposite side, then solve them simultaneously. Their intersection is the orthocenter; the third altitude passes through the same point.
Where is the orthocenter of a right triangle?
In a right triangle the orthocenter sits exactly at the right-angle vertex, because the two legs are themselves altitudes. In an acute triangle it lies inside, and in an obtuse triangle it lies outside.
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