← etc / Encyclopedia of Triangle Centers

X₂₈₅₆¶

SM(X₉₈, X₁₀₀)

X₂₈₅₆ (SM(X₉₈, X₁₀₀)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2856 = SM(X_98, X_100)."""

        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_02856(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2856 = SM(X_98, X_100) on reference triangle ABC."""
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center"])
            X_325 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)', ID="X_325", classes=["center"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center"])
            X_693 = eval_trilinear_point(model, A, B, C, '(b - c)/a**(2)', ID="X_693", classes=["center"])
            central_line(model, X_100, X_325, 100, 325)
            central_line(model, X_98, X_693, 98, 693)
            X_2856 = intersect_lines(model, X_100, X_325, X_98, X_693, ID="X_2856", classes=["selected", "target"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_1959 = eval_trilinear_point(model, A, B, C, '(cot(A))**(2) - cot(B)*cot(C)', ID="X_1959", classes=["center", "incident"])
            central_line(model, X_101, X_1959, 101, 1959, incident=True)
            return promote_point_to_top(model, X_2856)


        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_2856 on the given reference triangle."""
            model = create_model('X_2856 = SM(X_98, X_100)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02856(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-02856.json"))
            write_center_svg(
                model_acute,
                here / "x-02856.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2856¶

X₂₈₅₆¶