The orthocentre of a triangle is the point where all three altitudes of the triangle intersect. An altitude in a triangle is a perpendicular segment from a vertex to the line that contains the opposite side.
To better understand this, let’s consider the properties of the orthocentre:
- The orthocentre can be located inside the triangle, outside, or on the triangle itself, depending on the type of triangle:
- In an acute triangle, the orthocentre lies inside the triangle.
- In a right triangle, the orthocentre is at the vertex of the right angle.
- In an obtuse triangle, the orthocentre falls outside the triangle.
- The orthocentre is one of the triangle’s points of concurrency, along with the centroid, circumcentre, and incenter.
- The coordinates of the orthocentre can be calculated using the vertices of the triangle and applying certain geometric formulas.
Understanding the orthocentre is important in various fields such as geometry, architecture, and engineering, as it helps in analyzing the properties and behaviors of triangles.