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X₂₅₀₄¶

RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE}

X₂₅₀₄ (RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02504(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE} on reference triangle ABC."""
            X_2504 = eval_trilinear_point(model, A, B, C, '(b*c*(b - c)*(b**(2) + c**(2) - a**(2))*(2*a**(3) + (b + c)*(b - c - a)*(b - c + a)))', ID="X_2504", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_11, X_244, 11, 244, incident=True)
            X_441 = point_from_barycentrics(model, A, B, C, 0.74590002, 0.58940921, -0.33530923, ID="X_441", classes=["center", "incident"])
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center", "incident"])
            central_line(model, X_441, X_525, 441, 525, incident=True)
            X_2473 = eval_trilinear_point(model, A, B, C, '((b - c)*(a**(4) - (b + c)*a**(3) + 2*b*c*a**(2) - a*(b + c)**(3) + (b**(2) + c**(2))*(b - c)**(2)))', ID="X_2473", classes=["center", "incident"])
            X_2488 = eval_trilinear_point(model, A, B, C, '(a*(b + c - a)*(b - c)*((b - c)**(2) - a*b - a*c))', ID="X_2488", classes=["center", "incident"])
            central_line(model, X_2473, X_2488, 2473, 2488, incident=True)
            return promote_point_to_top(model, X_2504)


        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_2504 on the given reference triangle."""
            model = create_model('X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02504(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-02504.json"))
            write_center_svg(
                model_acute,
                here / "x-02504.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2504¶

X₂₅₀₄¶