← etc / Encyclopedia of Triangle Centers

X₂₄₈₁¶

INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE)

X₂₄₈₁ = Steiner-circumellipse-X₁-antipode of X₆₆₄

X₂₄₈₁ (INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2481 = INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE)."""

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


        def construct_x_02481(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2481 = INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE) on reference triangle ABC."""
            X_2223 = point_from_barycentrics(model, A, B, C, -0.97809077, -0.16901408, 2.1471049, ID="X_2223", classes=["center"])
            X_2481 = isogonal_conjugate(model, A, B, C, X_2223, ID="X_2481", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_8, X_76, 8, 76, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_9, X_75, 9, 75, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_1, X_85, 1, 85, incident=True)
            return promote_point_to_top(model, X_2481)


        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_2481 on the given reference triangle."""
            model = create_model('X_2481 = INTERSECTION(FEUERBACH HYPERBOLA, STEINER CIRCUMELLIPSE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02481(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-02481.json"))
            write_center_svg(
                model_acute,
                here / "x-02481.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2481¶

X₂₄₈₁¶