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X₉₃₅¶

POINT ALCOR

X₉₃₅ = trilinear pole of line X₆ X₆₇ (the radical axis of the orthocentroidal circle and Dao-Moses-Telv circle)

X₉₃₅ (POINT ALCOR) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_935 = POINT ALCOR."""

        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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00935(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_935 = POINT ALCOR on reference triangle ABC."""
            X_935 = eval_barycentric_point(model, A, B, C, '1/((b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2)))', ID="X_935", classes=["selected", "target"])
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_67, X_74, 67, 74, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_186 = eval_trilinear_point(model, A, B, C, '4*cos(A) - sec(A)', ID="X_186", classes=["center", "incident"])
            central_line(model, X_98, X_186, 98, 186, incident=True)
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_468 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cot(B) + cot(C) - 2*cot(A))', ID="X_468", classes=["center", "incident"])
            central_line(model, X_111, X_468, 111, 468, incident=True)
            return promote_point_to_top(model, X_935)


        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_935 on the given reference triangle."""
            model = create_model('X_935 = POINT ALCOR')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00935(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-00935.json"))
            write_center_svg(
                model_acute,
                here / "x-00935.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X935¶

X₉₃₅¶