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X₈₂₆¶

ODD (0, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₈₂₆ lies on the line at infinity.

X₈₂₆ (ODD (0, 4) INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_826 = ODD (0, 4) 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_barycentric_point,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00826(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_826 = ODD (0, 4) INFINITY POINT on reference triangle ABC."""
            X_826 = eval_trilinear_point(model, A, B, C, 'a **(-1)*(b**(4) - c**(4)) + a**(3)*(b**(0) - c**(0))', ID="X_826", 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_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_879 = eval_barycentric_point(model, A, B, C, '(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))/(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_879", classes=["center", "incident"])
            central_line(model, X_54, X_879, 54, 879, incident=True)
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_882 = point_from_barycentrics(model, A, B, C, 0.023590899, 1.0060979, -0.02968882, ID="X_882", classes=["center", "incident"])
            central_line(model, X_76, X_882, 76, 882, incident=True)
            return promote_point_to_top(model, X_826)


        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_826 on the given reference triangle."""
            model = create_model('X_826 = ODD (0, 4) INFINITY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00826(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-00826.json"))
            write_center_svg(
                model_acute,
                here / "x-00826.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X826¶

X₈₂₆¶