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X₁₂₀₅¶

3rd SARAGOSSA POINT OF X₆₇

X₁₂₀₅ (3rd SARAGOSSA POINT OF X₆₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1205 = 3rd SARAGOSSA POINT OF X_67."""

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


        def construct_x_01205(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1205 = 3rd SARAGOSSA POINT OF X_67 on reference triangle ABC."""
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center"])
            X_1177 = eval_trilinear_point(model, A, B, C, '(a/(b**(6) + c**(6) - a**(4)*b**(2) - a**(4)*c**(2) + 2*a**(2)*b**(2)*c**(2) - b**(4)*c**(2) - b**(2)*c**(4)))', ID="X_1177", classes=["center"])
            X_1205 = crosspoint(model, A, B, C, X_67, X_1177, ID="X_1205", classes=["selected", "target"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_74, X_511, 74, 511, incident=True)
            return promote_point_to_top(model, X_1205)


        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_1205 on the given reference triangle."""
            model = create_model('X_1205 = 3rd SARAGOSSA POINT OF X_67')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01205(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-01205.json"))
            write_center_svg(
                model_acute,
                here / "x-01205.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1205¶

X₁₂₀₅¶