In $\triangle ABC$, M is the midpoint of BC and A(X)(H)D is an altitude. Of course, a circle (actually is the “nine-point circle”) can be drawn through M, D, X.
If, in addition, AX = XH, can I conclude that H is the orthocenter? If that is not sufficient, what else do I need?
Besides M and D, need one more point (out of the remaining 7 points of the nine-point circle) to fix the circle. If the circle drawn cuts AD at X, then H, the ortho-center should be another point on and between AD such that AX = XH.