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X₂₇₃₅¶

SR(X₁₀₂, X₁₁₁)

X₂₇₃₅ = reflection of X₂₇₆₈ in X₃

X₂₇₃₅ (SR(X₁₀₂, X₁₁₁)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2735 = SR(X_102, 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02735(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2735 = SR(X_102, X_111) on reference triangle ABC."""
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center"])
            X_524 = eval_trilinear_point(model, A, B, C, '(2*a**(2) - b**(2) - c**(2))/a', ID="X_524", classes=["center"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center"])
            X_515 = eval_trilinear_point(model, A, B, C, '(b + c)*sec(A) - b*sec(B) - c*sec(C)', ID="X_515", classes=["center"])
            central_line(model, X_102, X_524, 102, 524)
            central_line(model, X_111, X_515, 111, 515)
            X_2735 = intersect_lines(model, X_102, X_524, X_111, X_515, ID="X_2735", classes=["selected", "target"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", 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_109, X_1499, 109, 1499, incident=True)
            return promote_point_to_top(model, X_2735)


        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_2735 on the given reference triangle."""
            model = create_model('X_2735 = SR(X_102, X_111)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02735(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-02735.json"))
            write_center_svg(
                model_acute,
                here / "x-02735.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2735¶

X₂₇₃₅¶