"""Programmatic construction for Book IV, Proposition 16 (IV.16)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0116.g1 (Inscribed regular fifteen-angled figure) using geometor.model."""
model = Model("IV.16")
# Points (y-inverted for standard mathematical coordinates)
O = model.set_point(153.00, -156.00, ID="O")
A = model.set_point(153.00, -30.00, classes=["given"], ID="A")
B = model.set_point(33.17, -117.06, ID="B")
E = model.set_point(27.69, -169.17, ID="E")
C = model.set_point(43.88, -219.00, ID="C")
D = model.set_point(262.12, -219.00, ID="D")
P2 = model.set_point(204.25, -40.89, ID="P2")
P3 = model.set_point(246.64, -71.69, ID="P3")
P4 = model.set_point(272.83, -117.06, ID="P4")
P5 = model.set_point(278.31, -169.17, ID="P5")
P7 = model.set_point(227.06, -257.94, ID="P7")
P8 = model.set_point(179.20, -279.25, ID="P8")
P9 = model.set_point(126.80, -279.25, ID="P9")
P10 = model.set_point(78.94, -257.94, ID="P10")
P14 = model.set_point(59.36, -71.69, ID="P14")
P15 = model.set_point(101.75, -40.89, ID="P15")
# Given circle ABCD
model.construct_circle(O, A)
# Segments
model.set_segment(A, C)
model.set_segment(C, D)
model.set_segment(D, A)
model.set_segment(A, B)
model.set_segment(B, E)
model.set_segment(E, C)
# Polygons
model.set_polygon([A, C, D])
model.set_polygon([A, P4, P7, P10, B])
model.set_polygon([A, P2, P3, P4, P5, D, P7, P8, P9, P10, C, E, B, P14, P15])
return model
if __name__ == "__main__":
construct_g1()
