← etc / Encyclopedia of Triangle Centers

X₃₇₆₅¶

X₈₆₉com[T(bc, c²)]

X₃₇₆₅ = anticomplement of X₃₇₅₉₆

X₃₇₆₅ (X₈₆₉com[T(bc, c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3765 = X_869com[T(bc, c²)]."""

        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_barycentric_point,
            eval_trilinear_point,
            nagel_point_of,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03765(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3765 = X_869com[T(bc, c²)] on reference triangle ABC."""
            X_3765 = eval_barycentric_point(model, A, B, C, 'b*c*(a**(3) + b**(2)*c + c**(2)*b)', ID="X_3765", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_4, X_8, 4, 8, incident=True)
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_239 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - b*c)', ID="X_239", classes=["center", "incident"])
            central_line(model, X_76, X_239, 76, 239, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_313 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(3)*c**(3)', ID="X_313", classes=["center", "incident"])
            central_line(model, X_6, X_313, 6, 313, incident=True)
            return promote_point_to_top(model, X_3765)


        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_3765 on the given reference triangle."""
            model = create_model('X_3765 = X_869com[T(bc, c²)]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03765(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-03765.json"))
            write_center_svg(
                model_acute,
                here / "x-03765.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3765¶

X₃₇₆₅¶