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X₁₁₉₉¶

3rd SARAGOSSA POINT OF X₅₄

X₁₁₉₉ (3rd SARAGOSSA POINT OF X₅₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1199 = 3rd SARAGOSSA POINT OF X_54."""

        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,
            crosspoint,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01199(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1199 = 3rd SARAGOSSA POINT OF X_54 on reference triangle ABC."""
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center"])
            X_1173 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(4) - 3*a**(2)*(b**(2) + c**(2)) + (b**(2) - c**(2))**(2))', ID="X_1173", classes=["center"])
            X_1199 = crosspoint(model, A, B, C, X_54, X_1173, ID="X_1199", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            central_line(model, X_23, X_143, 23, 143, incident=True)
            X_186 = eval_trilinear_point(model, A, B, C, '4*cos(A) - sec(A)', ID="X_186", classes=["center", "incident"])
            central_line(model, X_54, X_186, 54, 186, incident=True)
            return promote_point_to_top(model, X_1199)


        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_1199 on the given reference triangle."""
            model = create_model('X_1199 = 3rd SARAGOSSA POINT OF X_54')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01199(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-01199.json"))
            write_center_svg(
                model_acute,
                here / "x-01199.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1199¶

X₁₁₉₉¶