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X₅₇₀¶

ORTHOGONAL OF X₅₂

X₅₇₀ = inverse-in-Brocard-circle of X₅₇₁

X₅₇₀ (ORTHOGONAL OF X₅₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_570 = ORTHOGONAL OF X_52."""

        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,
            circumcenter_of,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00570(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_570 = ORTHOGONAL OF X_52 on reference triangle ABC."""
            X_311 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*cos(B - C)', ID="X_311", classes=["center"])
            X_570 = complement(model, A, B, C, X_311, ID="X_570", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_128 = eval_trilinear_point(model, A, B, C, '((sec(A))*(cos(2*B) + cos(2*C))*(1 + 2*cos(2*A))*(cos(2*A) + 2*cos(2*B)*cos(2*C)))', ID="X_128", classes=["center", "incident"])
            central_line(model, X_115, X_128, 115, 128, incident=True)
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center", "incident"])
            X_232 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(A +  omega  )', ID="X_232", classes=["center", "incident"])
            central_line(model, X_53, X_232, 53, 232, incident=True)
            return promote_point_to_top(model, X_570)


        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_570 on the given reference triangle."""
            model = create_model('X_570 = ORTHOGONAL OF X_52')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00570(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-00570.json"))
            write_center_svg(
                model_acute,
                here / "x-00570.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X570¶

X₅₇₀¶