Work out triangle orthocenter instantly with clear inputs, formula shown and shareable results.
The orthocentre H is where the three altitudes meet. Using the Euler line relation H = A + B + C − 2O, where O is the circumcentre, gives it directly without solving altitude equations.
Euler line relation
H = A + B + C − 2·O (O = circumcentre)
At the right-angle vertex, because two of the altitudes are the legs themselves.
The straight line through the orthocentre, centroid and circumcentre, with the centroid always between the other two in a 2:1 ratio.