"""Programmatic construction for Book III, Proposition 14 (III.14).
In a circle equal straight lines are equally distant from the centre,
and those which are equally distant from the centre are equal to one another.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0041.g1 using geometor.model."""
model = Model("III.14")
# Centre E of circle ABDC with radius 62
E = model.set_point(0, 0, classes=["given"], ID="E")
# Equal chords AB and CD at distance 36 from centre E
h = sp.sqrt(62**2 - 36**2)
G = model.set_point(36, 0, ID="G")
D = model.set_point(36, h, ID="D")
C = model.set_point(36, -h, ID="C")
# Circle ABDC
model.construct_circle(E, D)
# Chord AB rotated by -135 degrees so EF has length 36
inv_sqrt2 = sp.sqrt(2) / 2
F = model.set_point(-36 * inv_sqrt2, -36 * inv_sqrt2, ID="F")
B = model.set_point((-36 - h) * inv_sqrt2, (-36 + h) * inv_sqrt2, label="B")
A = model.set_point((-36 + h) * inv_sqrt2, (-36 - h) * inv_sqrt2, label="A")
# Chords AB and CD and their half-segments
model.set_segment(B, F)
model.set_segment(F, A)
model.set_segment(A, B)
model.set_section([A, F, B])
model.set_segment(D, G)
model.set_segment(G, C)
model.set_segment(C, D)
model.set_section([C, G, D])
# Perpendiculars EF, EG and radii AE, EC
model.set_segment(E, F)
model.set_segment(E, G)
model.set_segment(A, E)
model.set_segment(E, C)
# Right triangles EFA and EGC
model.set_polygon([E, F, A])
model.set_polygon([E, G, C])
return model
if __name__ == "__main__":
construct_g1()
