The center J_i of an excircle. There are three excenters for a given triangle, denoted J_1, J_2, J_3. The incenter I and excenters J_i of a triangle are an orthocentric system. (O I)^_ ^2 + (O J_1)^_ ^2 + (O J_2)^_ ^2 + (O J_3)^_ ^2 = 12R^2, where O is the circumcenter, J_i are the excenters, and R is the circumradius. Denote the midpoints of the original triangle M_1, M_2, and M_3. Then the lines J_1 M_1, J_2 M_2, and J_3 M_3 intersect in a point known as the mittenpunkt.

excenter-excenter circle | excentral triangle | excircles | incenter | mittenpunkt | orthocentric centroid