← etc / Encyclopedia of Triangle Centers

X₂₅₀₃¶

RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE}

X₂₅₀₃ (RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN 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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02503(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE} on reference triangle ABC."""
            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_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            X_2503 = ceva_conjugate(model, A, B, C, X_842, X_55, ID="X_2503", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_6, X_110, 6, 110, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_44, X_513, 44, 513, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_2611 = point_from_barycentrics(model, A, B, C, 0.21464646, 0.68065268, 0.10470085, ID="X_2611", classes=["center", "incident"])
            central_line(model, X_37, X_2611, 37, 2611, incident=True)
            return promote_point_to_top(model, X_2503)


        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_2503 on the given reference triangle."""
            model = create_model('X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02503(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-02503.json"))
            write_center_svg(
                model_acute,
                here / "x-02503.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2503¶

X₂₅₀₃¶