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X₁₁₉₀¶

2nd SARAGOSSA POINT OF X₅₅

X₁₁₉₀ (2nd SARAGOSSA POINT OF X₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1190 = 2nd SARAGOSSA POINT OF X_55."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01190(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1190 = 2nd SARAGOSSA POINT OF X_55 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            central_line(model, X_6, X_57, 6, 57)
            central_line(model, X_41, X_55, 41, 55)
            X_1190 = intersect_lines(model, X_6, X_57, X_41, X_55, ID="X_1190", classes=["selected", "target"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            X_218 = eval_trilinear_point(model, A, B, C, '((cos(A/2))**(2)*((cos(B/2))**(4) + (cos(C/2))**(4) - (cos(A/2))**(4)))', ID="X_218", classes=["center", "incident"])
            central_line(model, X_165, X_218, 165, 218, incident=True)
            return promote_point_to_top(model, X_1190)


        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_1190 on the given reference triangle."""
            model = create_model('X_1190 = 2nd SARAGOSSA POINT OF X_55')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01190(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-01190.json"))
            write_center_svg(
                model_acute,
                here / "x-01190.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1190¶

X₁₁₉₀¶