X(4)    ORTHOCENTER

The orthocenter, labeled 4, is the point of 
concurrence of the altitudes.

Sketch contributed by Michael Stairs,
January 2018.

Drag A, B, C.

4

A = (0.926111799297592, 4.223278802867947)
B = (-0.2573193160656448, 1.9093847328680538)
C = (3.641627457866125, 1.8472026016204806)
f = Segment(B, A)
g = Segment(A, C)
h = Segment(C, B)
i = AngularBisector(B, C, A)
j = AngularBisector(C, B, A)
C' = Midpoint(f)
B' = Midpoint(g)
A' = Midpoint(h)
m = OrthogonalLine(A', h)
D = Point(m)
k = OrthogonalLine(C, f)
l = OrthogonalLine(A, h)
n = OrthogonalLine(B, g)
E = Intersect(l, h)
p = Ray(E, A)
F = Intersect(k, n)