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X₂₁₁₈¶

POINT KEPLER VII

X₂₁₁₈ (POINT KEPLER VII) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2118 = POINT KEPLER VII."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02118(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2118 = POINT KEPLER VII on reference triangle ABC."""
            X_2118 = eval_trilinear_point(model, A, B, C, '(a*(a + b + c)*(b*c)**(1/2) + (b*c + c*a + a*b)*(a - (a*b)**(1/2) - (a*c)**(1/2)))', ID="X_2118", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_365 = eval_trilinear_point(model, A, B, C, 'a**(1/2)', ID="X_365", classes=["center", "incident"])
            central_line(model, X_6, X_365, 6, 365, incident=True)
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            X_2119 = eval_trilinear_point(model, A, B, C, '(a**(1/2)/((a + b + c)*(a*b*c)**(1/2) + (b*c + c*a + a*b)*(a**(1/2) - b**(1/2) - c**(1/2))))', ID="X_2119", classes=["center", "incident"])
            central_line(model, X_238, X_2119, 238, 2119, incident=True)
            X_2108 = eval_trilinear_point(model, A, B, C, '((b + c)*a**(3) - (b**(2) - b*c + c**(2))*a**(2) - (b + c)*(b**(2) + c**(2))*a + b*c*(b**(2) + b*c + c**(2)))', ID="X_2108", classes=["center", "incident"])
            X_2147 = point_from_barycentrics(model, A, B, C, 0.6235198, -0.91312312, 1.2896033, ID="X_2147", classes=["center", "incident"])
            central_line(model, X_2108, X_2147, 2108, 2147, incident=True)
            return promote_point_to_top(model, X_2118)


        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_2118 on the given reference triangle."""
            model = create_model('X_2118 = POINT KEPLER VII')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02118(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-02118.json"))
            write_center_svg(
                model_acute,
                here / "x-02118.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2118¶

X₂₁₁₈¶