← etc / Encyclopedia of Triangle Centers

X₁₁₇₀¶

1st SARAGOSSA POINT OF X₄₁

X₁₁₇₀ (1st SARAGOSSA POINT OF X₄₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1170 = 1st SARAGOSSA POINT OF X_41."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01170(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1170 = 1st SARAGOSSA POINT OF X_41 on reference triangle ABC."""
            X_1170 = eval_trilinear_point(model, A, B, C, '1/((a - b - c)*(a*(b + c) - (b - c)**(2)))', ID="X_1170", classes=["selected", "target"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_41, X_57, 41, 57, incident=True)
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            central_line(model, X_65, X_105, 65, 105, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_220 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)**(2)', ID="X_220", classes=["center", "incident"])
            central_line(model, X_2, X_220, 2, 220, incident=True)
            return promote_point_to_top(model, X_1170)


        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_1170 on the given reference triangle."""
            model = create_model('X_1170 = 1st SARAGOSSA POINT OF X_41')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01170(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-01170.json"))
            write_center_svg(
                model_acute,
                here / "x-01170.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1170¶

X₁₁₇₀¶