The orthocenter of triangle g is the point of intersection of the three altitudes of g

For a detailed description of the orthocenter H, use the routine detail (i.e., detail(H))

Note that the routine only works if the vertices of the triangle are known.

The command with(geometry,orthocenter) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{ps}≔\mathrm{point}\left(A\,0\,0\right),\mathrm{point}\left(B\,2\,0\right),\mathrm{point}\left(C\,1\,3\right)\:$

$\mathrm{triangle}\left(\mathrm{ABC}\,\left[\mathrm{ps}\right]\right)$

$\mathrm{ABC}$

$\mathrm{orthocenter}\left(H\,\mathrm{ABC}\right)$

$H$

$\mathrm{coordinates}\left(H\right)$

$\left[1\,\frac{1}{3}\right]$