The midpoints, foot points, midpoints from vertices and orthocenter
all lie on the circle.  Drag the vertices to change the triangle.

A = (0.86, 2.88)
B = (8.34, -1.98)
C = (-0.7000000000000001, -3.98)
poly1, c, a, b = Polygon(A, B, C)
d = Line(C, B)
e = Line(B, A)
f = Line(A, C)
D = Midpoint(A, C)
E = Midpoint(a)
F = Midpoint(c)
g = Segment(A, E)
h = Segment(B, D)
i = Segment(C, F)
G = Intersect(g, i)
j = OrthogonalLine(B, f)
k = OrthogonalLine(A, d)
l = OrthogonalLine(C, e)
H = Intersect(l, e)
I = Intersect(d, k)
J = Intersect(f, j)
p = Circle(D, F, E)
K = Intersect(k, j)
L = Midpoint(A, K)
M = Midpoint(C, K)
N = Midpoint(K, B)