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X₈₅₀¶

BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA

The barycentric product of X₈₅₀ and the circumcircle is the Kiepert hyperbola.

X₈₅₀ (BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_850 = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA."""

        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,
            isotomic_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00850(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_850 = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA on reference triangle ABC."""
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center"])
            X_850 = isotomic_conjugate(model, A, B, C, X_110, ID="X_850", classes=["selected", "target"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_476 = eval_trilinear_point(model, A, B, C, '1/((1 + 2*cos(2*A))*sin(B - C))', ID="X_476", classes=["center", "incident"])
            central_line(model, X_99, X_476, 99, 476, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center", "incident"])
            central_line(model, X_2, X_647, 2, 647, incident=True)
            X_685 = eval_trilinear_point(model, A, B, C, '(1/(sec(B)*(sin(C))**(3) - sec(C)*(sin(B))**(3)))', ID="X_685", classes=["center", "incident"])
            central_line(model, X_110, X_685, 110, 685, incident=True)
            return promote_point_to_top(model, X_850)


        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_850 on the given reference triangle."""
            model = create_model('X_850 = BARYCENTRIC MULTIPLIER FOR KIEPERT HYPERBOLA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00850(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-00850.json"))
            write_center_svg(
                model_acute,
                here / "x-00850.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X850¶

X₈₅₀¶