← etc / Encyclopedia of Triangle Centers

X₁₁₇₉¶

1st SARAGOSSA POINT OF X₉₆

X₁₁₇₉ (1st SARAGOSSA POINT OF X₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1179 = 1st SARAGOSSA POINT OF X_96."""

        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,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01179(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1179 = 1st SARAGOSSA POINT OF X_96 on reference triangle ABC."""
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center"])
            X_264 = eval_trilinear_point(model, A, B, C, 'csc(A)*csc(2*A)', ID="X_264", classes=["center"])
            X_93 = eval_trilinear_point(model, A, B, C, 'sec(3*A)', ID="X_93", classes=["center"])
            X_324 = eval_trilinear_point(model, A, B, C, 'b*c*sec(A)*cos(B - C)', ID="X_324", classes=["center"])
            central_line(model, X_24, X_264, 24, 264)
            central_line(model, X_93, X_324, 93, 324)
            X_1179 = intersect_lines(model, X_24, X_264, X_93, X_324, ID="X_1179", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_569 = point_from_barycentrics(model, A, B, C, 0.2994203, 0.35119708, 0.34938262, ID="X_569", classes=["center", "incident"])
            central_line(model, X_4, X_569, 4, 569, incident=True)
            return promote_point_to_top(model, X_1179)


        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_1179 on the given reference triangle."""
            model = create_model('X_1179 = 1st SARAGOSSA POINT OF X_96')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01179(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-01179.json"))
            write_center_svg(
                model_acute,
                here / "x-01179.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1179¶

X₁₁₇₉¶