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X₅₈₃¶

ORTHOGONAL OF X₅₀₀

X₅₈₃ = inverse-in-Brocard-circle of X₅₈₄

X₅₈₃ (ORTHOGONAL OF X₅₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_583 = ORTHOGONAL OF X_500."""

        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,
            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_00583(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_583 = ORTHOGONAL OF X_500 on reference triangle ABC."""
            X_583 = eval_trilinear_point(model, A, B, C, '(a*(a**(2)*b + a**(2)*c + 2*a*b*c - b**(3) - c**(3)))', ID="X_583", 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_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_38 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2)', ID="X_38", classes=["center", "incident"])
            central_line(model, X_37, X_38, 37, 38, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_992 = eval_trilinear_point(model, A, B, C, '(a**(3)*(b + c) + a**(2)*(b**(2) + c**(2)) - a*b*c*(b + c) - b*c*(b + c)**(2))', ID="X_992", classes=["center", "incident"])
            central_line(model, X_44, X_992, 44, 992, incident=True)
            return promote_point_to_top(model, X_583)


        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_583 on the given reference triangle."""
            model = create_model('X_583 = ORTHOGONAL OF X_500')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00583(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-00583.json"))
            write_center_svg(
                model_acute,
                here / "x-00583.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X583¶

X₅₈₃¶