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X₂₆₇₉¶

RS(X₉₈, X₉₉)

X₂₆₇₉ is the center of the rectangular hyperbola that passes through the points A, B, C, and X₃₂.

X₂₆₇₉ (RS(X₉₈, X₉₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2679 = RS(X_98, X_99)."""

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


        def construct_x_02679(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2679 = RS(X_98, X_99) on reference triangle ABC."""
            X_2679 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))**(2)*(a**(4) - b**(2)*c**(2))*(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2)))', ID="X_2679", classes=["selected", "target"])
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center", "incident"])
            central_line(model, X_114, X_325, 114, 325, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_115, X_512, 115, 512, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_805 = eval_trilinear_point(model, A, B, C, '(1/(a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))))', ID="X_805", classes=["center", "incident"])
            central_line(model, X_2, X_805, 2, 805, incident=True)
            return promote_point_to_top(model, X_2679)


        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_2679 on the given reference triangle."""
            model = create_model('X_2679 = RS(X_98, X_99)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02679(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-02679.json"))
            write_center_svg(
                model_acute,
                here / "x-02679.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2679¶

X₂₆₇₉¶