Evans's theorem

Evans's theorem states that in a simple triangle, the three centers known as the centroid (where medians meet), the orthocenter (where altitudes intersect), and the circumcenter (center of the circumscribed circle) all lie along a single straight line called the Euler line. Moreover, these points are distinct unless the triangle is equilateral. This theorem highlights a special and elegant relationship between key triangle centers, revealing underlying geometric harmony and offering insight into the triangle’s shape and properties.