← etc / Encyclopedia of Triangle Centers

X₂₇₁₃¶

SR(X₉₉, X₁₀₇)

X₂₇₁₃ = reflection of X₂₇₀₆ in X₃

X₂₇₁₃ (SR(X₉₉, X₁₀₇)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2713 = SR(X_99, X_107)."""

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


        def construct_x_02713(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2713 = SR(X_99, X_107) on reference triangle ABC."""
            X_2706 = point_from_barycentrics(model, A, B, C, 1.0408365, 0.2875314, -0.32836793, ID="X_2706", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_2713 = reflection_in_point(model, X_2706, X_3, ID="X_2713", classes=["selected", "target"], guide=False)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_520 = eval_trilinear_point(model, A, B, C, '(cos(A))*(sin(2*B) - sin(2*C))', ID="X_520", classes=["center", "incident"])
            central_line(model, X_99, X_520, 99, 520, incident=True)
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_107, X_512, 107, 512, incident=True)
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            X_1294 = eval_barycentric_point(model, A, B, C, '1/(a**(6)*(b**(2) + c**(2)) - a**(4)*(3*b**(4) - 4*b**(2)*c**(2) + 3*c**(4)) + 3*a**(2)*(b**(2) - c**(2))**(2)*(b**(2) + c**(2)) - (b**(2) - c**(2))**(2)*(b**(4) + 4*b**(2)*c**(2) + c**(4)))', ID="X_1294", classes=["center", "incident"])
            central_line(model, X_511, X_1294, 511, 1294, incident=True)
            return promote_point_to_top(model, X_2713)


        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_2713 on the given reference triangle."""
            model = create_model('X_2713 = SR(X_99, X_107)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02713(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-02713.json"))
            write_center_svg(
                model_acute,
                here / "x-02713.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2713¶

X₂₇₁₃¶