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X₂₉₃₉¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₄

X₂₉₃₉ is the excentral-isogonal conjugate of X₄.

X₂₉₃₉ (EXCENTRAL-ISOGONAL CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2939 = EXCENTRAL-ISOGONAL CONJUGATE OF X_4."""

        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,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02939(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2939 = EXCENTRAL-ISOGONAL CONJUGATE OF X_4 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2360 = point_from_barycentrics(model, A, B, C, 0.53385863, 0.53888318, -0.072741807, ID="X_2360", classes=["center"])
            X_2939 = reflection_in_point(model, X_1, X_2360, ID="X_2939", classes=["selected", "target"], guide=False)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            central_line(model, X_1, X_19, 1, 19, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            central_line(model, X_43, X_46, 43, 46, incident=True)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_228 = eval_trilinear_point(model, A, B, C, '(sin(2*A))*(sin(B) + sin(C))', ID="X_228", classes=["center", "incident"])
            central_line(model, X_35, X_228, 35, 228, incident=True)
            return promote_point_to_top(model, X_2939)


        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_2939 on the given reference triangle."""
            model = create_model('X_2939 = EXCENTRAL-ISOGONAL CONJUGATE OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02939(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-02939.json"))
            write_center_svg(
                model_acute,
                here / "x-02939.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2939¶

X₂₉₃₉¶