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X₂₉₀₆¶

ORTHIC-ISOGONAL CONJUGATE OF X₂₈

X₂₉₀₆ is the orthic-isogonal conjugate of X₂₈.

X₂₉₀₆ (ORTHIC-ISOGONAL CONJUGATE OF X₂₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2906 = ORTHIC-ISOGONAL CONJUGATE OF X_28."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02906(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2906 = ORTHIC-ISOGONAL CONJUGATE OF X_28 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_28 = eval_trilinear_point(model, A, B, C, '(tan(A))/(b + c)', ID="X_28", classes=["center"])
            X_2906 = ceva_conjugate(model, A, B, C, X_4, X_28, ID="X_2906", classes=["selected", "target"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_28, X_60, 28, 60, incident=True)
            X_193 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cot(B) + cot(C) - cot(A))', ID="X_193", classes=["center", "incident"])
            X_406 = eval_trilinear_point(model, A, B, C, '(b*c*(a + b + c) + a*b*c*sec(A))', ID="X_406", classes=["center", "incident"])
            central_line(model, X_193, X_406, 193, 406, incident=True)
            X_1029 = eval_trilinear_point(model, A, B, C, '(1/(a + 2*(a + b + c)*cos(A)))', ID="X_1029", classes=["center", "incident"])
            central_line(model, X_4, X_1029, 4, 1029, incident=True)
            return promote_point_to_top(model, X_2906)


        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_2906 on the given reference triangle."""
            model = create_model('X_2906 = ORTHIC-ISOGONAL CONJUGATE OF X_28')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02906(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-02906.json"))
            write_center_svg(
                model_acute,
                here / "x-02906.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2906¶

X₂₉₀₆¶