← etc / Encyclopedia of Triangle Centers

X₁₄₆₃¶

X₇₂₆-BETH CONJUGATE OF X₇₂₆

X₁₄₆₃ (X₇₂₆-BETH CONJUGATE OF X₇₂₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1463 = X_726-BETH CONJUGATE OF X_726."""

        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,
            gergonne_point_of,
            nagel_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01463(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1463 = X_726-BETH CONJUGATE OF X_726 on reference triangle ABC."""
            X_1447 = point_from_barycentrics(model, A, B, C, -0.76119403, 0.059701493, 1.7014925, ID="X_1447", classes=["center"])
            X_241 = eval_trilinear_point(model, A, B, C, '(cos(B/2))**(4) - ((cos(A/2))**(2))*((cos(B/2))**(2) +(cos(C/2))**(2)) + (cos(C/2))**(4)', ID="X_241", classes=["center"])
            X_1463 = ceva_conjugate(model, A, B, C, X_1447, X_241, ID="X_1463", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_7, X_8, 7, 8, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_87 = eval_trilinear_point(model, A, B, C, '1/(a*b + a*c - b*c)', ID="X_87", classes=["center", "incident"])
            central_line(model, X_56, X_87, 56, 87, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_583 = eval_trilinear_point(model, A, B, C, '(a*(a**(2)*b + a**(2)*c + 2*a*b*c - b**(3) - c**(3)))', ID="X_583", classes=["center", "incident"])
            central_line(model, X_44, X_583, 44, 583, incident=True)
            return promote_point_to_top(model, X_1463)


        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_1463 on the given reference triangle."""
            model = create_model('X_1463 = X_726-BETH CONJUGATE OF X_726')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01463(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-01463.json"))
            write_center_svg(
                model_acute,
                here / "x-01463.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1463¶

X₁₄₆₃¶