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X₃₄₃₁¶

X₄-VERTEX CONJUGATE OF X₆

X₃₄₃₁ (X₄-VERTEX CONJUGATE OF X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3431 = X_4-VERTEX CONJUGATE OF X_6."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03431(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3431 = X_4-VERTEX CONJUGATE OF X_6 on reference triangle ABC."""
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center"])
            X_3431 = isogonal_conjugate(model, A, B, C, X_381, ID="X_3431", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", 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_6, X_186, 6, 186, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_265 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*csc(3*A)', ID="X_265", classes=["center", "incident"])
            central_line(model, X_2, X_265, 2, 265, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_323 = eval_trilinear_point(model, A, B, C, 'sin(3*A)*(csc(A))**(2)', ID="X_323", classes=["center", "incident"])
            central_line(model, X_3, X_323, 3, 323, incident=True)
            return promote_point_to_top(model, X_3431)


        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_3431 on the given reference triangle."""
            model = create_model('X_3431 = X_4-VERTEX CONJUGATE OF X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03431(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-03431.json"))
            write_center_svg(
                model_acute,
                here / "x-03431.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3431¶

X₃₄₃₁¶