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X₃₄₄₉¶

1st SARAGOSSA POINT OF X₇

Saragossa points are discussed just before X₁₁₆₆.

X₃₄₄₉ (1st SARAGOSSA POINT OF X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3449 = 1st SARAGOSSA POINT OF X_7."""

        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,
            gergonne_point_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03449(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3449 = 1st SARAGOSSA POINT OF X_7 on reference triangle ABC."""
            X_2886 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(3) + c**(3) - a*b**(2) - a*c**(2) - b**(2)*c - b*c**(2)))', ID="X_2886", classes=["center"])
            X_3449 = isogonal_conjugate(model, A, B, C, X_2886, ID="X_3449", classes=["selected", "target"])
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center", "incident"])
            X_672 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - a*(b + c))', ID="X_672", classes=["center", "incident"])
            central_line(model, X_572, X_672, 572, 672, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1602 = point_from_barycentrics(model, A, B, C, 0.24316346, 0.2467371, 0.51009944, ID="X_1602", classes=["center", "incident"])
            central_line(model, X_6, X_1602, 6, 1602, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_2175 = eval_trilinear_point(model, A, B, C, '(cot(A/2)*(sin(A))**(3))', ID="X_2175", classes=["center", "incident"])
            central_line(model, X_7, X_2175, 7, 2175, incident=True)
            return promote_point_to_top(model, X_3449)


        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_3449 on the given reference triangle."""
            model = create_model('X_3449 = 1st SARAGOSSA POINT OF X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03449(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-03449.json"))
            write_center_svg(
                model_acute,
                here / "x-03449.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3449¶

X₃₄₄₉¶