"""Programmatic construction for Book III, Proposition 13 (III.13).
A circle does not touch a circle at more points than one, whether it touch
it internally or externally.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0038.g3 using geometor.model."""
model = Model("III.13")
# Circle ABDC (true center O1) and line of hypothetical internal contacts BGHD
O1 = model.set_point(0, 58, classes=["auxiliary"])
B = model.set_point(-sp.sqrt(3036), 0, label="B")
D = model.set_point(sp.sqrt(3036), 0, label="D")
model.construct_circle(O1, B)
# Assumed centres G and H on chord BD
G = model.set_point(-20, 0, classes=["given"], ID="G")
H = model.set_point(20, 0, classes=["given"], ID="H")
model.construct_line(B, D)
# Points E and F on inner oval EBFD
E = model.set_point(0, 80, ID="E")
F = model.set_point(0, -14, ID="F")
model.construct_circle(H, D)
# External circle ACK touching/cutting ABDC at A and C
O2 = model.set_point(86, 146, classes=["auxiliary"])
A = model.set_point(34, 130, ID="A")
C = model.set_point(71, 94, ID="C")
K = model.set_point(140, 146, ID="K")
model.construct_circle(O2, A)
# Collinear segments along BGHD
model.set_segment(B, G)
model.set_segment(G, H)
model.set_segment(H, D)
model.set_segment(B, H)
model.set_segment(G, D)
model.set_segment(B, D)
model.set_section([B, G, D])
model.set_section([B, H, D])
# Chord AC joining points of external contact A and C
model.set_segment(A, C)
return model
if __name__ == "__main__":
construct_g1()
