There are two different definitions of the mid-arc points. The mid-arc points M_(A B), M_(A C), and M_(B C) of a triangle Δ A B C as defined by Johnson are the points on the circumcircle of the triangle which lie half-way along each of the three arcs determined by the vertices. These points arise in the definition of the Fuhrmann circle and Fuhrmann triangle, and lie on the extensions of the perpendicular bisectors of the triangle sides drawn from the circumcenter O.

arc | circumcircle mid-arc triangle | cyclic quadrilateral | first mid-arc point | Fuhrmann center | Fuhrmann circle | Fuhrmann triangle | mid-arc triangle | perspector | second mid-arc point | third mid-arc point