← etc / Encyclopedia of Triangle Centers

X₂₀₁₆¶

EXSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE)

X₂₀₁₆ is the exsimilicenter(gallatly circle, orthocentroidal circle).

X₂₀₁₆ (EXSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2016 = EXSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE)."""

        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_02016(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2016 = EXSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE) on reference triangle ABC."""
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center"])
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center"])
            X_1344 = eval_trilinear_point(model, A, B, C, '( OH  + R)*cos(A) + 4*R*cos(B)*cos(C)', ID="X_1344", classes=["center"])
            X_1690 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  /2 -  pi  /4)', ID="X_1690", classes=["center"])
            central_line(model, X_39, X_381, 39, 381)
            central_line(model, X_1344, X_1690, 1344, 1690)
            X_2016 = intersect_lines(model, X_39, X_381, X_1344, X_1690, ID="X_2016", classes=["selected", "target"])
            X_1345 = eval_trilinear_point(model, A, B, C, '( OH  - R)*cos(A) - 4*R*cos(B)*cos(C)', ID="X_1345", classes=["center", "incident"])
            X_1689 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  /2 +  pi  /4)', ID="X_1689", classes=["center", "incident"])
            central_line(model, X_1345, X_1689, 1345, 1689, incident=True)
            return promote_point_to_top(model, X_2016)


        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_2016 on the given reference triangle."""
            model = create_model('X_2016 = EXSIMILICENTER(GALLATLY CIRCLE, ORTHOCENTROIDAL CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02016(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-02016.json"))
            write_center_svg(
                model_acute,
                here / "x-02016.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2016¶

X₂₀₁₆¶