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X₇₆₉¶

o-(- 4, - 3) CIRCUMCIRCLE POINT

1/[\(a^{m-1}(b^{n} - c^{n})\) + \(a^{n-1}(b^{m} - c^{m})\)],

hence the name “(m, n)-circumcircle point”.

X₇₆₉ (o-(- 4, - 3) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_769 = o-(- 4, - 3) CIRCUMCIRCLE POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00769(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_769 = o-(- 4, - 3) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_768 = eval_trilinear_point(model, A, B, C, '(a **(-5)*(b **(-3) - c **(-3)) + a **(-4)*(b **(-4) - c **(-4)))', ID="X_768", classes=["center"])
            X_769 = isogonal_conjugate(model, A, B, C, X_768, ID="X_769", classes=["selected", "target"])
            return promote_point_to_top(model, X_769)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_769 on the given reference triangle."""
            model = create_model('X_769 = o-(- 4, - 3) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00769(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-00769.json"))
            write_center_svg(
                model_acute,
                here / "x-00769.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X769¶

X₇₆₉¶