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X₂₇₀₉¶

SR(X₉₈, X₁₁₁)

X₂₇₀₉ = reflection of X₈₄₃ in X₃

X₂₇₀₉ (SR(X₉₈, X₁₁₁)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2709 = SR(X_98, X_111)."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02709(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2709 = SR(X_98, X_111) on reference triangle ABC."""
            X_843 = point_from_barycentrics(model, A, B, C, 0.55581336, -0.33333326, 0.77751991, ID="X_843", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_2709 = reflection_in_point(model, X_843, X_3, ID="X_2709", classes=["selected", "target"], guide=False)
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_352 = eval_trilinear_point(model, A, B, C, '(a*(-a**(4) - b**(4) - c**(4) - 5*b**(2)*c**(2) + 4*a**(2)*b**(2) + 4*a**(2)*c**(2)))', ID="X_352", classes=["center", "incident"])
            central_line(model, X_111, X_352, 111, 352, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_524 = eval_trilinear_point(model, A, B, C, '(2*a**(2) - b**(2) - c**(2))/a', ID="X_524", classes=["center", "incident"])
            central_line(model, X_98, X_524, 98, 524, incident=True)
            central_line(model, X_3, X_843, 3, 843, incident=True)
            return promote_point_to_top(model, X_2709)


        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_2709 on the given reference triangle."""
            model = create_model('X_2709 = SR(X_98, X_111)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02709(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-02709.json"))
            write_center_svg(
                model_acute,
                here / "x-02709.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2709¶

X₂₇₀₉¶