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X₂₇₆₇¶

SR(X₁₀₈, X₁₁₁)

X₂₇₆₇ (SR(X₁₀₈, X₁₁₁)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2767 = SR(X_108, 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_02767(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2767 = SR(X_108, X_111) on reference triangle ABC."""
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", 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_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center"])
            central_line(model, X_108, X_524, 108, 524)
            central_line(model, X_111, X_521, 111, 521)
            X_2767 = intersect_lines(model, X_108, X_524, X_111, X_521, ID="X_2767", classes=["selected", "target"])
            X_691 = eval_trilinear_point(model, A, B, C, 'a/((b**(2) - c**(2))*(2*a**(2) - b**(2) - c**(2)))', ID="X_691", classes=["center", "incident"])
            X_1812 = eval_trilinear_point(model, A, B, C, 'cot(A)*cot(A/2)/(b + c)', ID="X_1812", classes=["center", "incident"])
            central_line(model, X_691, X_1812, 691, 1812, incident=True)
            return promote_point_to_top(model, X_2767)


        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_2767 on the given reference triangle."""
            model = create_model('X_2767 = SR(X_108, X_111)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02767(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-02767.json"))
            write_center_svg(
                model_acute,
                here / "x-02767.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2767¶

X₂₇₆₇¶