← etc / Encyclopedia of Triangle Centers

X₂₈₆₈¶

SM(X₁₁₀, X₁₁₁)

X₂₈₆₈ (SM(X₁₁₀, X₁₁₁)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2868 = SM(X_110, 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_02868(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2868 = SM(X_110, X_111) on reference triangle ABC."""
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center"])
            X_385 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - b**(2)*c**(2))', ID="X_385", classes=["center"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center"])
            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"])
            central_line(model, X_112, X_385, 112, 385)
            central_line(model, X_76, X_691, 76, 691)
            X_2868 = intersect_lines(model, X_112, X_385, X_76, X_691, ID="X_2868", classes=["selected", "target"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_805 = eval_trilinear_point(model, A, B, C, '(1/(a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))))', ID="X_805", classes=["center", "incident"])
            central_line(model, X_69, X_805, 69, 805, incident=True)
            return promote_point_to_top(model, X_2868)


        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_2868 on the given reference triangle."""
            model = create_model('X_2868 = SM(X_110, X_111)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02868(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-02868.json"))
            write_center_svg(
                model_acute,
                here / "x-02868.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2868¶

X₂₈₆₈¶