"""Programmatic construction for Book III, Proposition 17 (III.17).
From a given point to draw a straight line touching a given circle.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book III, Proposition 17 using geometor.model."""
model = Model("III.17")
# 1. Let A be the given point, and BCD the given circle about centre E.
E = model.set_point(0, 0, classes=["given"], ID="E")
D = model.set_point(0, 1, classes=["given"], ID="D")
C = model.set_point(1, 0, ID="C")
r_outer = sp.Rational(45, 29)
A = model.set_point(0, r_outer, classes=["given"], ID="A")
circle_BCD = model.construct_circle(E, D)
# 2. Let AE be joined, and with centre E and distance EA describe circle AFG.
model.set_segment(E, D)
model.set_segment(D, A)
model.set_segment(A, E)
model.set_section([E, D, A])
circle_AFG = model.construct_circle(E, A)
# 3. From D draw DF at right angles to EA meeting circle AFG at F.
fx = -sp.sqrt(r_outer**2 - 1)
F = model.set_point(fx, 1, ID="F")
G = model.set_point(sp.Rational(34, 29), -sp.sqrt(r_outer**2 - sp.Rational(34, 29) ** 2), label="G")
model.set_segment(D, F)
# 4. Join EF (cutting circle BCD at B) and join AB.
B = model.set_point(fx / r_outer, 1 / r_outer, ID="B")
model.set_segment(E, B)
model.set_segment(B, F)
model.set_segment(E, F)
model.set_section([E, B, F])
model.set_segment(A, B)
# 5. Triangles DEF and BEA
model.set_polygon([D, E, F])
model.set_polygon([B, E, A])
return model
if __name__ == "__main__":
construct_g1()
