G.139 Thales’ theorem and angles in circle segments — Code¶
In a circle, the angle in a semicircle is right, the angle in a greater segment is acute, and the angle in a lesser segment is obtuse.
"""Programmatic construction for Book III, Proposition 31 (III.31)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0068.g1 using geometor.model."""
model = Model("III.31")
# Circle center E, points A, B, C, D on circle, and produced point F (y-inverted)
E = model.set_point(129.00, -103.00, ID="E")
A = model.set_point(52.19, -89.46, classes=["given"], ID="A")
B = model.set_point(101.05, -175.82, classes=["given"], ID="B")
C = model.set_point(156.95, -30.18, classes=["given"], ID="C")
D = model.set_point(76.81, -45.03, classes=["given"], ID="D")
F = model.set_point(25.32, -41.96, ID="F")
# Circle ABCD
model.construct_circle(E, A)
# Segments and sections
model.set_segment(B, C)
model.set_segment(B, E)
model.set_segment(E, C)
model.set_segment(B, A)
model.set_segment(A, F)
model.set_segment(B, F)
model.set_segment(A, C)
model.set_segment(A, D)
model.set_segment(D, C)
model.set_segment(A, E)
model.set_section([B, E, C])
model.set_section([B, A, F])
# Polygons
model.set_polygon([A, B, C, D])
model.set_polygon([A, B, C])
model.set_polygon([A, B, E])
model.set_polygon([A, C, E])
model.set_polygon([A, D, C])
# Angles (wedges)
model.set_wedge(A, B, B, C)
model.set_wedge(B, A, A, C)
model.set_wedge(D, A, A, C)
model.set_wedge(A, B, B, E)
model.set_wedge(C, A, A, E)
model.set_wedge(A, C, C, E)
model.set_wedge(A, F, F, C)
model.set_wedge(E, A, A, C)
model.set_wedge(E, A, A, B)
return model
if __name__ == "__main__":
construct_g1()