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X₂₉₇₈¶

RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE}

X₂₉₇₈ (RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY 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_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02978(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE} on reference triangle ABC."""
            X_785 = eval_trilinear_point(model, A, B, C, '(1/(a **(-4)*(b **(-2) - c **(-2)) + a **(-3)*(b **(-3) - c **(-3))))', ID="X_785", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_2978 = ceva_conjugate(model, A, B, C, X_785, X_6, ID="X_2978", classes=["selected", "target"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_320 = eval_trilinear_point(model, A, B, C, '(1 - 2*cos(A))/a**(2)', ID="X_320", classes=["center", "incident"])
            X_350 = eval_trilinear_point(model, A, B, C, '(a**(2) - b*c)*b**(2)*c**(2)', ID="X_350", classes=["center", "incident"])
            central_line(model, X_320, X_350, 320, 350, incident=True)
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            X_788 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(3) - c**(3))', ID="X_788", classes=["center", "incident"])
            central_line(model, X_661, X_788, 661, 788, incident=True)
            return promote_point_to_top(model, X_2978)


        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_2978 on the given reference triangle."""
            model = create_model('X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02978(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-02978.json"))
            write_center_svg(
                model_acute,
                here / "x-02978.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2978¶

X₂₉₇₈¶