G.590 equilateral triangle inscribed — Code

XIII.12

If an :term:`equilateral triangle <G.13>` be :term:`inscribed in a circle <G.148>`, the :term:`square <G.63>` on the side of the :term:`triangle <G.12>` is triple of the square on the radius of the :term:`circle <G.10>`.

"""Programmatic construction for Book XIII, Proposition 12 (XIII.12).

        Equilateral triangle ABC inscribed in circle ABC with centre D, diameter AE,
        and chord BE.
        """

        from __future__ import annotations

        import math
        from geometor.model import Model


        def construct_g1() -> Model:
            """Construct the figure 0471.g1 using geometor.model."""
            model = Model("XIII.12")

            cx, cy, r = 98.0, -114.0, 85.0
            D = model.set_point(cx, cy, classes=["given"], ID="D")

            # Equilateral triangle vertices A (top), B (bottom-left), C (bottom-right)
            angles_deg = [90.0, -150.0, -30.0]
            labels = ["A", "B", "C"]
            pts = {}
            for lbl, deg in zip(labels, angles_deg):
                rad = math.radians(deg)
                pts[lbl] = model.set_point(
                    round(cx + r * math.cos(rad), 1),
                    round(cy + r * math.sin(rad), 1),
                    classes=["given"],
                    label=lbl,
                )

            A, B, C = pts["A"], pts["B"], pts["C"]

            # Circle ABC
            model.construct_circle(D, A)

            # Diameter endpoint E at bottom (-90 deg)
            E = model.set_point(98.0, -199.0, classes=["constructed"], ID="E")

            # Polygons
            model.set_polygon([A, B, C])
            model.set_polygon([A, B, E])

            # Segments and collinear sub-segments
            for p1, p2 in [
                (A, B), (B, C), (C, A),
                (A, E), (A, D), (D, E),
                (B, E),
            ]:
                model.set_segment(p1, p2)

            # Section
            model.set_section([A, D, E])

            return model


        if __name__ == "__main__":
            construct_g1()