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X₂₇₅₇¶

SR(X₁₀₆, X₁₀₉)

X₂₇₅₇ = reflection of X₂₇₃₁ in X₃

X₂₇₅₇ (SR(X₁₀₆, X₁₀₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2757 = SR(X_106, X_109)."""

        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,
            nagel_point_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02757(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2757 = SR(X_106, X_109) on reference triangle ABC."""
            X_2731 = point_from_barycentrics(model, A, B, C, 0.039772765, 1.0340909, -0.073863689, ID="X_2731", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_2757 = reflection_in_point(model, X_2731, X_3, ID="X_2757", classes=["selected", "target"], guide=False)
            X_106 = eval_trilinear_point(model, A, B, C, 'a/(2*a - b - c)', ID="X_106", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_106, X_522, 106, 522, incident=True)
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            X_519 = eval_trilinear_point(model, A, B, C, '(2*a - b - c)/a', ID="X_519", classes=["center", "incident"])
            central_line(model, X_109, X_519, 109, 519, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_901 = eval_trilinear_point(model, A, B, C, 'a/((b - c)*(b + c - 2*a))', ID="X_901", classes=["center", "incident"])
            central_line(model, X_8, X_901, 8, 901, incident=True)
            return promote_point_to_top(model, X_2757)


        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_2757 on the given reference triangle."""
            model = create_model('X_2757 = SR(X_106, X_109)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02757(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-02757.json"))
            write_center_svg(
                model_acute,
                here / "x-02757.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2757¶

X₂₇₅₇¶