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X₇₈₈¶

ODD (- 3, 0) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₈₈ lies on the line at infinity.

X₇₈₈ (ODD (- 3, 0) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_788 = ODD (- 3, 0) INFINITY POINT."""

        from __future__ import annotations

        from pathlib import Path

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

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


        def construct_x_00788(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_788 = ODD (- 3, 0) INFINITY POINT on reference triangle ABC."""
            X_788 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(3) - c**(3))', ID="X_788", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_649 = eval_trilinear_point(model, A, B, C, 'a*(b - c)', ID="X_649", classes=["center", "incident"])
            central_line(model, X_42, X_649, 42, 649, incident=True)
            X_667 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b - c)', ID="X_667", classes=["center", "incident"])
            X_798 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(2) - c**(2))', ID="X_798", classes=["center", "incident"])
            central_line(model, X_667, X_798, 667, 798, incident=True)
            return promote_point_to_top(model, X_788)


        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_788 on the given reference triangle."""
            model = create_model('X_788 = ODD (- 3, 0) INFINITY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00788(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-00788.json"))
            write_center_svg(
                model_acute,
                here / "x-00788.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X788¶

X₇₈₈¶