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X₅₀₅¶

3rd ISOSCELIZER POINT

The isoscelizer equations H(A,X)D(A,X) = H(B,X)D(B,X) = H(C,X)D(C,X) have solution X = X₅₀₅. (Peter Yff, 4/9/99)

X₅₀₅ (3rd ISOSCELIZER POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_505 = 3rd ISOSCELIZER POINT."""

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


        def construct_x_00505(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_505 = 3rd ISOSCELIZER POINT on reference triangle ABC."""
            X_164 = eval_trilinear_point(model, A, B, C, 'sin(B/2) + sin(C/2) - sin(A/2)', ID="X_164", classes=["center"])
            X_505 = isogonal_conjugate(model, A, B, C, X_164, ID="X_505", classes=["selected", "target"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            central_line(model, X_40, X_164, 40, 164, incident=True)
            X_173 = eval_trilinear_point(model, A, B, C, 'cos(B/2) + cos(C/2) - cos(A/2)', ID="X_173", classes=["center", "incident"])
            X_1130 = eval_trilinear_point(model, A, B, C, '(sin(( pi  + 3*A)/4)/sin(( pi  - A)/4))', ID="X_1130", classes=["center", "incident"])
            central_line(model, X_173, X_1130, 173, 1130, incident=True)
            return promote_point_to_top(model, X_505)


        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_505 on the given reference triangle."""
            model = create_model('X_505 = 3rd ISOSCELIZER POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00505(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-00505.json"))
            write_center_svg(
                model_acute,
                here / "x-00505.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X505¶

X₅₀₅¶