G.135 equal chords cut off equal arcs — Code

III.28

In equal circles, equal chords cut off equal arcs, the greater equal to the greater and the less to the less.
A B C G K D E F H L 
"""Programmatic construction for Book III, Proposition 28 (III.28)."""

        from __future__ import annotations

        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0065.g1 using geometor.model."""
            model = Model("III.28")

            # Left circle ABC with center K and arc points C, G (y-inverted)
            K = model.set_point(73.00, -75.00, ID="K")
            A = model.set_point(25.30, -108.00, classes=["given"], ID="A")
            B = model.set_point(120.70, -108.00, classes=["given"], ID="B")
            C = model.set_point(73.00, -17.00, ID="C")
            G = model.set_point(73.00, -133.00, ID="G")

            # Right circle DEF with center L and arc points F, H (y-inverted)
            L = model.set_point(313.00, -75.00, ID="L")
            D = model.set_point(265.30, -108.00, classes=["given"], ID="D")
            E = model.set_point(360.70, -108.00, classes=["given"], ID="E")
            F = model.set_point(313.00, -17.00, ID="F")
            H = model.set_point(313.00, -133.00, ID="H")

            # Equal circles ABC and DEF
            model.construct_circle(K, A)
            model.construct_circle(L, D)

            # Segments
            model.set_segment(A, B)
            model.set_segment(A, K)
            model.set_segment(K, B)

            model.set_segment(D, E)
            model.set_segment(D, L)
            model.set_segment(L, E)

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

            # Angles (wedges)
            model.set_wedge(K, A, A, B)
            model.set_wedge(L, D, D, E)

            return model


        if __name__ == "__main__":
            construct_g1()