G.151 circumscribe a triangle about a circle equiangular with a triangle — Code

IV.3

Circumscribe about a given circle a triangle equiangular with a given triangle.
M L N A B C K H F E G D 
"""Programmatic construction for Book IV, Proposition 3 (IV.3)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0089.g1 using geometor.model."""
            model = Model("IV.3")

            # Points (y-inverted for standard mathematical coordinates)
            K = model.set_point(153.00, -104.00, ID="K")
            A = model.set_point(125.30, -68.54, ID="A")
            B = model.set_point(192.73, -82.87, ID="B")
            C = model.set_point(153.00, -149.00, ID="C")
            L = model.set_point(22.31, -149.00, ID="L")
            M = model.set_point(167.56, -35.52, ID="M")
            N = model.set_point(227.89, -149.00, ID="N")

            # Given triangle DEF and extended line HG
            D = model.set_point(320.00, -43.00, classes=["given"], ID="D")
            E = model.set_point(247.94, -99.30, classes=["given"], ID="E")
            F = model.set_point(218.00, -43.00, classes=["given"], ID="F")
            G = model.set_point(265.78, -132.85, ID="G")
            H = model.set_point(209.55, -27.11, ID="H")

            # Circle ABC
            model.construct_circle(K, A)

            # Construction lines
            model.construct_line(L, M)
            model.construct_line(M, N)
            model.construct_line(N, L)
            model.construct_line(H, G)

            # Segments
            model.set_segment(L, M)
            model.set_segment(M, N)
            model.set_segment(N, L)
            model.set_segment(L, A)
            model.set_segment(A, M)
            model.set_segment(M, B)
            model.set_segment(B, N)
            model.set_segment(N, C)
            model.set_segment(C, L)
            model.set_segment(K, A)
            model.set_segment(K, B)
            model.set_segment(K, C)
            model.set_segment(D, E)
            model.set_segment(E, F)
            model.set_segment(F, D)
            model.set_segment(E, G)
            model.set_segment(F, H)
            model.set_segment(H, G)

            # Collinear sections
            model.set_section([L, A, M])
            model.set_section([M, B, N])
            model.set_section([N, C, L])
            model.set_section([H, F, E])
            model.set_section([F, E, G])

            # Polygons
            model.set_polygon([L, M, N])
            model.set_polygon([D, E, F])
            model.set_polygon([A, M, B, K])

            # Angles (wedges)
            model.set_wedge(K, B, B, A)
            model.set_wedge(K, B, B, C)
            model.set_wedge(K, C, C, A)
            model.set_wedge(A, K, K, M)
            model.set_wedge(B, K, K, M)
            model.set_wedge(M, A, A, B)
            model.set_wedge(N, L, L, B)
            model.set_wedge(L, M, M, N)
            model.set_wedge(E, D, D, G)
            model.set_wedge(E, D, D, F)
            model.set_wedge(F, D, D, H)
            model.set_wedge(F, D, D, E)
            model.set_wedge(D, E, E, F)

            return model


        if __name__ == "__main__":
            construct_g1()