G.144 tangent-secant theorem — Code¶
If from a point outside a circle a secant and a tangent are drawn, the rectangle contained by the whole secant and its external segment equals the square on the tangent.
g1.py
"""Programmatic construction for Book III, Proposition 36 Case 1 (III.36 - g1)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0080.g1 using geometor.model."""
model = Model("III.36.g1")
# Circle ABC with center F(84, -74), radius 58 (y-inverted)
F = model.set_point(84.0, -74.0, ID="F")
B = model.set_point(26.0, -74.0, classes=["given"], ID="B")
D = model.set_point(26.0, -152.0, classes=["given"], ID="D")
C = model.set_point(49.39, -120.54, ID="C")
A = model.set_point(118.61, -27.46, ID="A")
# Circle ABC
model.construct_circle(F, B)
# Segments
model.set_segment(A, D)
model.set_segment(A, C)
model.set_segment(A, F)
model.set_segment(F, C)
model.set_segment(C, D)
model.set_segment(F, D)
model.set_segment(D, B)
model.set_segment(F, B)
# Sections
model.set_section([D, C, A])
model.set_section([D, C, F])
model.set_section([C, F, A])
model.set_section([D, F, A])
# Polygon and angle
model.set_polygon([F, B, D])
model.set_wedge(B, F, F, D)
return model
if __name__ == "__main__":
construct_g1()
g2.py
"""Programmatic construction for Book III, Proposition 36 Case 2 (III.36 - g2)."""
from __future__ import annotations
from geometor.model import Model
def construct_g2() -> Model:
"""Construct the figure 0080.g2 using geometor.model."""
model = Model("III.36.g2")
# Circle ABC with center E(138, -70), radius 54 (y-inverted)
E = model.set_point(138.0, -70.0, ID="E")
B = model.set_point(138.0, -124.0, classes=["given"], ID="B")
D = model.set_point(24.0, -128.33, classes=["given"], ID="D")
C = model.set_point(104.66, -112.47, ID="C")
F = model.set_point(144.80, -104.58, ID="F")
A = model.set_point(184.94, -96.69, ID="A")
# Circle ABC
model.construct_circle(E, B)
# Segments
model.set_segment(A, D)
model.set_segment(A, C)
model.set_segment(A, F)
model.set_segment(F, C)
model.set_segment(C, D)
model.set_segment(F, D)
model.set_segment(D, B)
model.set_segment(E, B)
model.set_segment(E, F)
model.set_segment(E, C)
model.set_segment(E, D)
# Sections
model.set_section([D, C, A])
model.set_section([D, C, F])
model.set_section([C, F, A])
model.set_section([D, F, A])
# Polygons
model.set_polygon([E, B, D])
model.set_polygon([E, F, C])
model.set_polygon([E, F, D])
# Angles
model.set_wedge(B, E, E, D)
model.set_wedge(F, E, E, C)
return model
if __name__ == "__main__":
construct_g2()