Archimedes Conoids P.7
Author: John H. McCoy
Date: 31 July 2013

Base Center

Show Geometrical Solution

Show Right Angle Solution

Archimedes Proposition 7
Three solutions

CB = 4.2 (slider from 0 to 5, step 0.1)
CA = 6.4 (slider from CB to 8, step 0.1)
C = (4.7, -2.92)
c = Circle(C, CB)
B'_1 = Point(c)
a_1 = Line(C, B'_1)
B = Intersect(c, a_1, 2)
b = OrthogonalLine(C, a_1)
CO = 7.3 (slider from 0 to 15, step 0.1)
d = Circle(C, CO)
O = Intersect(d, b, 2)
e = Ray(O, B)
f = Ray(O, B'_1)
B' = Intersect(f, a_1)
D = Point(f)
j = Ray(B, D)
E = Intersect(b, j)
l = Segment(B, E)
m = Segment(E, D)
F_1 = Midpoint(B, D)
A_1 = Point(b)
h = CircleArc(A_1, B', B)
A = Point(h)
i = Segment(C, A)
poly1, b', o, b_1 = Polygon(O, B, B')
poly2, d_1, b_2, b'_1 = Polygon(B, B', D)
rCB: CB^(2) / CA^(2)
p = Circle(B', ((rCB * 2) * CB))
BE = Distance(B, E)
ED = Distance(E, D)
OE = Distance(O, E)
testlight: CA^(2) / CO^(2) - (BE * ED / OE^(2))
M = (-6.379040126414121, -2.5585479199278653)
N = (-6.358327395167815, -5.5945124250467275)
s = Circle(M, N)
t = Line(N, M)
M' = Rotate(M, testlight, N)
α = Angle(M, N, M')
c_1 = Line(N, M')
P_1 = Intersect(s, c_1, 2)
Q = Intersect(s, t, 2)
e_1 = Segment(N, P_1)
f_1 = Line(E, i)
k_1 = Line(O, A)
A' = Intersect(f_1, k_1)
l_1 = Segment(O, A')
m_1 = Segment(E, A')
a = Segment(A, A')
u: abs(((2 * CB) * rCB))
S = Point(Circle[B, abs(((2 * CB) * rCB))])
j_1 = Segment(B, S)
n_1 = Line(S, b_1)
T = Intersect(n_1, e)
n = Segment(T, S)
g = CircumcircleArc(B, O, B')
v = false
OC = Distance(O, C)
q_1 = Circle(C, CA)
k = Segment(B, B')
q = Line(T, j_1)
F = Intersect(g, q, 2)
r = Segment(O, F)
g_1 = Segment(T, F)
G = Point(f)
h_1 = Line(C, G)
H = Intersect(h_1, e)
i_1 = OrthogonalLine(C, h_1)
I = Intersect(q_1, i_1, 2)
p_1 = Ray(I, H)
H' = Rotate(H, 90*°, I)
β = Angle(H, I, H')
r_1 = Ray(I, H')
J = Intersect(h_1, r_1)
K_1 = Point(p_1)
s_1 = Segment(I, K_1)
L = Point(r_1)
t_1 = Segment(I, L)
a_2 = Segment(H, J)
c_2 = Segment(C, I)
w = false
R = Point(h_1)
U = Point(h_1)
d_2 = Segment(R, U)
e_2 = CircumcircleArc(B, A', D)
V = Center(h)
W = Center(g)
f_2 = Line(C, r)
P = Intersect(e, f_2)
K = Intersect(f_2, f)
g_2 = Segment(P, K)