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X₂₄₉₃¶

RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE}

X₂₄₉₃ (RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE}."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            crosspoint,
            eval_barycentric_point,
            eval_trilinear_point,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02493(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_842 = eval_barycentric_point(model, A, B, C, 'a**(2)/(2*a**(6) - 2*a**(4)*(b**(2) + c**(2)) + a**(2)*(b**(4) + c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2)))', ID="X_842", classes=["center"])
            X_2493 = crosspoint(model, A, B, C, X_2, X_842, ID="X_2493", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_5, X_39, 5, 39, 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_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center", "incident"])
            central_line(model, X_23, X_50, 23, 50, incident=True)
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_2, X_94, 2, 94, incident=True)
            return promote_point_to_top(model, X_2493)


        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_2493 on the given reference triangle."""
            model = create_model('X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02493(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-02493.json"))
            write_center_svg(
                model_acute,
                here / "x-02493.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2493¶

X₂₄₉₃¶