Challenge 41: The Orthocenter of a Triangle
- Gerry Stahl
The “orthocenter” of a triangle is the meeting point of the three altitudes of the triangle. An “altitude” of a triangle is the segment that is perpendicular to a side and goes to the opposite vertex. If you consider the four points consisting of the triangle’s three vertices and the orthocenter, then the orthocenter of any triangle formed by three of those points will be the fourth point. Can you see why this is true?