Sentence:  Every triangle has a <WSD>midcircle</WSD>, and its center is the fourth kind of middle point that a triangle can have. In 1767 Leonhard Euler proved that for all triangles, the orthocenter, the circumcenter, the centroid and the center of the <WSD>midcircle</WSD> are always on the same line. 
Meaning of the word marked with <WSD> tags:  (geometry) The circle (if one exists) that passes through the midpoint of each side of a given polygon, especially a triangle.