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X₂₇₄₀¶

SR(X₁₀₃, X₁₁₁)

X₂₇₄₀ = reflection of X₂₇₂₉ in X₃

X₂₇₄₀ (SR(X₁₀₃, X₁₁₁)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2740 = SR(X_103, 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_02740(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2740 = SR(X_103, X_111) on reference triangle ABC."""
            X_2729 = point_from_barycentrics(model, A, B, C, 0.71174829, -0.30626744, 0.59451916, ID="X_2729", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_2740 = reflection_in_point(model, X_2729, X_3, ID="X_2740", classes=["selected", "target"], guide=False)
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", 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_103, X_524, 103, 524, incident=True)
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_111, X_516, 111, 516, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_1499 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))*(b**(2) + c**(2) - 5*a**(2))', ID="X_1499", classes=["center", "incident"])
            central_line(model, X_101, X_1499, 101, 1499, incident=True)
            return promote_point_to_top(model, X_2740)


        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_2740 on the given reference triangle."""
            model = create_model('X_2740 = SR(X_103, X_111)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02740(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-02740.json"))
            write_center_svg(
                model_acute,
                here / "x-02740.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2740¶

X₂₇₄₀¶