"""Programmatic construction for Book I, Proposition 11 (I.11).
To draw a straight line at right angles to a given straight line from a given
point on it.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book I, Proposition 11 using geometor.model."""
model = Model("I.11")
# 1. Given straight line AB and given point C on it
A = model.set_point(-sp.Rational(3, 2), 0, classes=["given"], label="A")
B = model.set_point(sp.Rational(3, 2), 0, classes=["given"], label="B")
C = model.set_point(0, 0, classes=["given"], ID="C")
model.construct_line(A, B)
# 2. Take point D at random on AC, and make CE equal to CD [I. 3]
D = model.set_point(-1, 0, ID="D")
E = model.set_point(1, 0, ID="E")
model.set_segment(A, D)
model.set_segment(D, C)
model.set_segment(A, C)
model.set_segment(C, E)
model.set_segment(E, B)
model.set_segment(C, B)
model.set_segment(D, E)
model.set_segment(A, B)
# 3. Construct equilateral triangle FDE on DE [I. 1] and join FC
F = model.set_point(0, sp.sqrt(3), label="F")
model.set_segment(D, F)
model.set_segment(E, F)
model.set_segment(F, C)
model.set_polygon([F, D, E])
model.set_polygon([D, F, C])
model.set_polygon([E, F, C])
return model
if __name__ == "__main__":
construct_g1()
