← etc / Encyclopedia of Triangle Centers

X₁₄₃₂¶

X₂₅₇-BETH CONJUGATE OF X₂₅₇

X₁₄₃₂ (X₂₅₇-BETH CONJUGATE OF X₂₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1432 = X_257-BETH CONJUGATE OF X_257."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            incenter_of,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01432(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1432 = X_257-BETH CONJUGATE OF X_257 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_257 = eval_trilinear_point(model, A, B, C, '1/(a**(3) + a*b*c)', ID="X_257", classes=["center"])
            central_line(model, X_1, X_256, 1, 256)
            central_line(model, X_2, X_257, 2, 257)
            X_1432 = intersect_lines(model, X_1, X_256, X_2, X_257, ID="X_1432", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_330 = eval_trilinear_point(model, A, B, C, 'b*c/(a*b + a*c - b*c)', ID="X_330", classes=["center", "incident"])
            central_line(model, X_7, X_330, 7, 330, incident=True)
            return promote_point_to_top(model, X_1432)


        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_1432 on the given reference triangle."""
            model = create_model('X_1432 = X_257-BETH CONJUGATE OF X_257')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01432(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-01432.json"))
            write_center_svg(
                model_acute,
                here / "x-01432.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1432¶

X₁₄₃₂¶