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X₁₁₆₇¶

1st SARAGOSSA POINT OF X₃₄

X₁₁₆₇ (1st SARAGOSSA POINT OF X₃₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1167 = 1st SARAGOSSA POINT OF X_34."""

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


        def construct_x_01167(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1167 = 1st SARAGOSSA POINT OF X_34 on reference triangle ABC."""
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center"])
            X_255 = eval_trilinear_point(model, A, B, C, '(cos(A))**(2)', ID="X_255", classes=["center"])
            X_269 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)', ID="X_269", classes=["center"])
            central_line(model, X_34, X_40, 34, 40)
            central_line(model, X_255, X_269, 255, 269)
            X_1167 = intersect_lines(model, X_34, X_40, X_255, X_269, ID="X_1167", classes=["selected", "target"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_580 = point_from_barycentrics(model, A, B, C, 0.002197609, 0.25263713, 0.74516526, ID="X_580", classes=["center", "incident"])
            central_line(model, X_56, X_580, 56, 580, incident=True)
            return promote_point_to_top(model, X_1167)


        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_1167 on the given reference triangle."""
            model = create_model('X_1167 = 1st SARAGOSSA POINT OF X_34')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01167(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-01167.json"))
            write_center_svg(
                model_acute,
                here / "x-01167.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1167¶

X₁₁₆₇¶