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X₂₅₃₀¶

RADICAL CENTER OF {BROCARD, BEVAN, (X₄,2R)} CIRCLES

X₂₅₃₀ = reflection of X₆₆₇ and X₉₀₅

X₂₅₃₀ (RADICAL CENTER OF {BROCARD, BEVAN, (X₄,2R)} CIRCLES) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2530 = RADICAL CENTER OF {BROCARD, BEVAN, (X_4,2R)} CIRCLES."""

        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,
            crosspoint,
            eval_trilinear_point,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02530(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2530 = RADICAL CENTER OF {BROCARD, BEVAN, (X_4,2R)} CIRCLES on reference triangle ABC."""
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center"])
            X_693 = eval_trilinear_point(model, A, B, C, '(b - c)/a**(2)', ID="X_693", classes=["center"])
            X_2530 = crosspoint(model, A, B, C, X_513, X_693, ID="X_2530", classes=["selected", "target"])
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            central_line(model, X_36, X_238, 36, 238, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            central_line(model, X_10, X_514, 10, 514, incident=True)
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            central_line(model, X_661, X_665, 661, 665, incident=True)
            return promote_point_to_top(model, X_2530)


        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_2530 on the given reference triangle."""
            model = create_model('X_2530 = RADICAL CENTER OF {BROCARD, BEVAN, (X_4,2R)} CIRCLES')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02530(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-02530.json"))
            write_center_svg(
                model_acute,
                here / "x-02530.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2530¶

X₂₅₃₀¶