"""Programmatic construction for Book XII, Proposition 2 (XII.2).
Circles ABCD and EFGH with diameters BD and FH, inscribed octagons AOBPCQDR
and EKFLGMHN, inscribed square EFGH, tangent rectangle on EF at K, and
auxiliary areas S and T.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0375.g1 using geometor.model."""
model = Model("XII.2")
# Left circle ABCD (center O1 = (111, -114), radius 88)
O1 = model.set_point(111.0, -114.0, ID="O1")
A = model.set_point(111.0, -26.0, classes=["given"], ID="A")
B = model.set_point(23.0, -114.0, classes=["given"], ID="B")
C = model.set_point(111.0, -202.0, classes=["given"], ID="C")
D = model.set_point(199.0, -114.0, classes=["given"], ID="D")
O = model.set_point(48.77, -51.77, ID="O")
P = model.set_point(48.77, -176.23, ID="P")
Q = model.set_point(173.23, -176.23, ID="Q")
R = model.set_point(173.23, -51.77, ID="R")
# Middle circle EFGH (center O2 = (327, -121), radius 73.5)
O2 = model.set_point(327.0, -121.0, ID="O2")
E = model.set_point(327.0, -47.5, classes=["given"], ID="E")
F = model.set_point(253.5, -121.0, classes=["given"], ID="F")
G = model.set_point(327.0, -194.5, classes=["given"], ID="G")
H = model.set_point(400.5, -121.0, classes=["given"], ID="H")
K = model.set_point(275.03, -69.03, ID="K")
L = model.set_point(275.03, -172.97, ID="L")
M = model.set_point(378.97, -172.97, ID="M")
N = model.set_point(378.97, -69.03, ID="N")
# Outer corners of tangent rectangle on EF at K
U = model.set_point(238.28, -105.78, ID="U")
V = model.set_point(311.78, -32.28, ID="V")
# Area S rectangle corners and center label point
S1 = model.set_point(442.0, -54.0, ID="S1")
S2 = model.set_point(525.0, -54.0, ID="S2")
S3 = model.set_point(525.0, -216.0, ID="S3")
S4 = model.set_point(442.0, -216.0, ID="S4")
S = model.set_point(483.5, -135.0, classes=["given"], ID="S")
# Area T rectangle corners and center label point
T1 = model.set_point(555.0, -70.0, ID="T1")
T2 = model.set_point(636.0, -70.0, ID="T2")
T3 = model.set_point(636.0, -178.0, ID="T3")
T4 = model.set_point(555.0, -178.0, ID="T4")
T = model.set_point(595.5, -124.0, classes=["given"], ID="T")
# Circles
model.construct_circle(O1, A)
model.construct_circle(O2, E)
# Segments in left circle
for p1, p2 in [
(B, D),
(A, O), (O, B), (B, P), (P, C), (C, Q), (Q, D), (D, R), (R, A),
]:
model.set_segment(p1, p2)
# Segments in middle circle
for p1, p2 in [
(F, H),
(E, F), (F, G), (G, H), (H, E),
(E, K), (K, F), (F, L), (L, G), (G, M), (M, H), (H, N), (N, E),
(F, U), (U, V), (V, E),
]:
model.set_segment(p1, p2)
# Polygons
model.set_polygon([A, O, B, P, C, Q, D, R])
model.set_polygon([E, F, G, H])
model.set_polygon([E, K, F, L, G, M, H, N])
model.set_polygon([E, K, F])
model.set_polygon([F, L, G])
model.set_polygon([G, M, H])
model.set_polygon([H, N, E])
model.set_polygon([F, U, V, E])
model.set_polygon([S1, S2, S3, S4])
model.set_polygon([T1, T2, T3, T4])
return model
if __name__ == "__main__":
construct_g1()
