middlespoint

The mittenpunkt (also called the middlespoint) of a triangle Δ A B C is the symmedian point of the excentral triangle, i.e., the point of concurrence M of the lines from the excenters J_i through the corresponding triangle side midpoints M_i. It is commonly denoted D or M, has equivalent triangle center functions α | = | b + c - a α | = | cot(1/2 A), and is Kimberling center X_9.

excenter | excentral triangle | isogonal mittenpunkt | Mandart inellipse | Nagel point