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X₂₉₅₃¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₆₂

X₂₉₅₃ is the excentral-isogonal conjugate of X₆₂.

X₂₉₅₃ (EXCENTRAL-ISOGONAL CONJUGATE OF X₆₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2953 = EXCENTRAL-ISOGONAL CONJUGATE OF X_62."""

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


        def construct_x_02953(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2953 = EXCENTRAL-ISOGONAL CONJUGATE OF X_62 on reference triangle ABC."""
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center"])
            X_1277 = eval_trilinear_point(model, A, B, C, '(sqrt(3/4) - sin(A -  pi  /3) + sin(B -  pi  /3) + sin(C -  pi  /3))', ID="X_1277", classes=["center"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center"])
            X_2945 = point_from_barycentrics(model, A, B, C, 0.54021963, 0.41139336, 0.048387008, ID="X_2945", classes=["center"])
            central_line(model, X_191, X_1277, 191, 1277)
            central_line(model, X_40, X_2945, 40, 2945)
            X_2953 = intersect_lines(model, X_191, X_1277, X_40, X_2945, ID="X_2953", classes=["selected", "target"])
            X_1761 = point_from_barycentrics(model, A, B, C, 0.54015296, 0.3957935, 0.064053537, ID="X_1761", classes=["center", "incident"])
            X_2321 = point_from_barycentrics(model, A, B, C, 0.47272727, 0.32727273, 0.2, ID="X_2321", classes=["center", "incident"])
            central_line(model, X_1761, X_2321, 1761, 2321, incident=True)
            return promote_point_to_top(model, X_2953)


        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_2953 on the given reference triangle."""
            model = create_model('X_2953 = EXCENTRAL-ISOGONAL CONJUGATE OF X_62')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02953(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-02953.json"))
            write_center_svg(
                model_acute,
                here / "x-02953.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2953¶

X₂₉₅₃¶