"""Programmatic construction for Book III, Proposition 21 (III.21).
In a circle the angles in the same segment 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 for Book III, Proposition 21 using geometor.model."""
model = Model("III.21")
# 1. Circle ABCD about centre F
F = model.set_point(0, 0, classes=["given"], ID="F")
C = model.set_point(0, -1, ID="C")
circle_ABCD = model.construct_circle(F, C)
# Points B, D, A, E on circumference
bx = sp.Rational(-61, 82)
by = -sp.sqrt(1 - bx**2)
B = model.set_point(bx, by, classes=["given"], ID="B")
D = model.set_point(-bx, by, classes=["given"], ID="D")
ax = sp.Rational(-33, 82)
ay = sp.sqrt(1 - ax**2)
A = model.set_point(ax, ay, classes=["given"], ID="A")
ey = sp.Rational(12, 82)
ex = sp.sqrt(1 - ey**2)
E = model.set_point(ex, ey, classes=["given"], ID="E")
# 2. Chords AB, AD, EB, ED, BD and radii BF, FD
model.set_segment(A, B)
model.set_segment(A, D)
model.set_segment(E, B)
model.set_segment(E, D)
model.set_segment(B, D)
model.set_segment(B, F)
model.set_segment(F, D)
model.set_polygon([B, A, D])
model.set_polygon([B, E, D])
model.set_polygon([B, F, D])
return model
if __name__ == "__main__":
construct_g1()
