Diagonals Cut - Exterior Edition

Drag the points of the quadrilateral to make the diagonals "special"

A = (-1, 2)
B = (-1, 4)
C = (5.5, 4)
D = (5.5, 2)
poly1, a, b, c, d = Polygon(A, B, C, D)
f = Line(B, D)
g = Line(A, C)
E = Intersect(f, g)
h = Segment(B, E)
i = Segment(C, E)
j = Segment(D, E)
k = Segment(A, E)
F = (-4, 2)
G = (-3, 2)
l = Segment(F, G)
H: (x(G) - 1 / 3, y(G))
I: (x(F) + 1 / 3, y(F))
m = OrthogonalLine(F, l)
n = OrthogonalLine(H, l)
p = OrthogonalLine(G, l)
q = OrthogonalLine(I, l)
e = Circle(F, h)
r = Circle(H, i)
s = Circle(I, j)
t = Circle(G, k)
J = Intersect(r, n, 2)
K = Intersect(e, m, 2)
L = Intersect(t, p, 2)
M = Intersect(s, q, 2)
f_1 = Segment(K, F)
g_1 = Segment(J, H)
h_1 = Segment(M, I)
i_1 = Segment(L, G)
c_1 = Circle(F, Distance[B, D])
d_1 = Circle(I, Distance[B, D])
e_1 = Circle(H, Distance[A, C])
k_1 = Circle(G, Distance[A, C])
N = Intersect(d_1, h_1, 1)
O = Intersect(c_1, f_1, 1)
P = Intersect(k_1, i_1, 1)
Q = Intersect(e_1, g_1, 1)
p_1 = Circle(C, D, A)