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X₃₅₉₄¶

ISOGONAL CONJUGATE OF 2nd DIXIT POINT

X₃₅₉₄ is the isogonal conjugate of 2nd dixit point.

X₃₅₉₄ (ISOGONAL CONJUGATE OF 2nd DIXIT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3594 = ISOGONAL CONJUGATE OF 2nd DIXIT 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03594(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3594 = ISOGONAL CONJUGATE OF 2nd DIXIT POINT on reference triangle ABC."""
            X_3594 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) - a**(2) - 6*area ))', ID="X_3594", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            X_546 = eval_trilinear_point(model, A, B, C, '3*cos(B - C) - 2*cos(A)', ID="X_546", classes=["center", "incident"])
            central_line(model, X_486, X_546, 486, 546, incident=True)
            X_615 = eval_trilinear_point(model, A, B, C, '(a**(2) - 4*area )/a', ID="X_615", classes=["center", "incident"])
            X_1587 = eval_trilinear_point(model, A, B, C, '(sin(A) + cos(B)*cos(C))', ID="X_1587", classes=["center", "incident"])
            central_line(model, X_615, X_1587, 615, 1587, incident=True)
            return promote_point_to_top(model, X_3594)


        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_3594 on the given reference triangle."""
            model = create_model('X_3594 = ISOGONAL CONJUGATE OF 2nd DIXIT POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03594(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-03594.json"))
            write_center_svg(
                model_acute,
                here / "x-03594.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3594¶

X₃₅₉₄¶