G.100 diameter bisects chord iff perpendicular — Code¶
A segment through the center of a circle bisects a chord not through the center if and only if it cuts the chord at right angles.
"""Programmatic construction for Book III, Proposition 3 (III.3)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0016.g1 using geometor.model."""
model = Model("III.3")
# Points (y-inverted for standard mathematical coordinates)
E = model.set_point(93, -104, ID="E")
C = model.set_point(93, -28, classes=["given"], ID="C")
D = model.set_point(93, -180, classes=["given"], ID="D")
F = model.set_point(93, -140, ID="F")
A = model.set_point(26.07, -140, classes=["given"], ID="A")
B = model.set_point(159.93, -140, classes=["given"], ID="B")
# Construction circle ABC
model.construct_circle(E, C)
# Segments
model.set_segment(C, D)
model.set_segment(A, B)
model.set_segment(E, A)
model.set_segment(E, B)
model.set_segment(A, F)
model.set_segment(F, B)
model.set_segment(F, E)
model.set_segment(C, E)
model.set_segment(E, D)
model.set_segment(C, F)
model.set_segment(F, D)
# Sections
model.set_section([A, F, B])
model.set_section([C, E, D])
model.set_section([C, F, D])
# Polygons
model.set_polygon([E, A, F])
model.set_polygon([E, B, F])
model.set_polygon([E, A, B])
# Angles (wedges)
model.set_wedge(F, A, A, E)
model.set_wedge(F, E, E, B)
model.set_wedge(A, E, E, F)
model.set_wedge(B, F, F, E)
return model
if __name__ == "__main__":
construct_g1()