"""Programmatic construction for Book XII, Proposition 1 (XII.1).
Similar polygons ABCDE and FGHKL inscribed in circles ABC and FGH with
diameters BM and GN.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0373.g1 using geometor.model."""
model = Model("XII.1")
# Left circle ABC (center O1 = (114, -111), radius 88)
O1 = model.set_point(114.0, -111.0, ID="O1")
A = model.set_point(108.0, -23.2, classes=["given"], ID="A")
B = model.set_point(28.5, -90.0, classes=["given"], ID="B")
C = model.set_point(81.0, -192.6, classes=["given"], ID="C")
D = model.set_point(186.0, -161.6, classes=["given"], ID="D")
E = model.set_point(199.3, -89.2, classes=["given"], ID="E")
M = model.set_point(199.5, -132.0, ID="M")
# Right circle FGH (center O2 = (370, -113), radius 70)
O2 = model.set_point(370.0, -113.0, ID="O2")
F = model.set_point(365.2, -43.2, classes=["given"], ID="F")
G = model.set_point(302.0, -96.3, classes=["given"], ID="G")
H = model.set_point(343.8, -177.9, classes=["given"], ID="H")
K = model.set_point(427.3, -153.2, classes=["given"], ID="K")
L = model.set_point(437.8, -95.6, classes=["given"], ID="L")
N = model.set_point(438.0, -129.7, ID="N")
# Circles
model.construct_circle(O1, A)
model.construct_circle(O2, F)
# Left segments
for p1, p2 in [
(A, B), (B, C), (C, D), (D, E), (E, A),
(B, E), (B, M), (A, M),
]:
model.set_segment(p1, p2)
# Right segments
for p1, p2 in [
(F, G), (G, H), (H, K), (K, L), (L, F),
(G, L), (G, N), (F, N),
]:
model.set_segment(p1, p2)
# Polygons and triangles
model.set_polygon([A, B, C, D, E])
model.set_polygon([F, G, H, K, L])
model.set_polygon([A, B, E])
model.set_polygon([F, G, L])
model.set_polygon([A, B, M])
model.set_polygon([F, G, N])
# Angles (wedges)
model.set_wedge(A, B, B, E)
model.set_wedge(F, G, G, L)
model.set_wedge(E, A, A, B)
model.set_wedge(L, F, F, G)
model.set_wedge(M, A, A, B)
model.set_wedge(N, F, F, G)
model.set_wedge(A, B, B, M)
model.set_wedge(F, G, G, N)
return model
if __name__ == "__main__":
construct_g1()
