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X₂₄₈₇¶

RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}

X₂₄₈₇ (RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER 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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02487(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} on reference triangle ABC."""
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center"])
            X_2487 = ceva_conjugate(model, A, B, C, X_37, X_523, ID="X_2487", classes=["selected", "target"])
            X_649 = eval_trilinear_point(model, A, B, C, 'a*(b - c)', ID="X_649", classes=["center", "incident"])
            X_1638 = eval_barycentric_point(model, A, B, C, '(b - c)*(2*a**(2) - b**(2) - c**(2) - a*b - a*c + 2*b*c)', ID="X_1638", classes=["center", "incident"])
            central_line(model, X_649, X_1638, 649, 1638, incident=True)
            X_1125 = eval_trilinear_point(model, A, B, C, '(2*a+b+c)/a', ID="X_1125", classes=["center", "incident"])
            X_1499 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))*(b**(2) + c**(2) - 5*a**(2))', ID="X_1499", classes=["center", "incident"])
            central_line(model, X_1125, X_1499, 1125, 1499, incident=True)
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            X_2516 = eval_trilinear_point(model, A, B, C, '((b - c)*(5*a - 3*b -3*c))', ID="X_2516", classes=["center", "incident"])
            central_line(model, X_514, X_2516, 514, 2516, incident=True)
            return promote_point_to_top(model, X_2487)


        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_2487 on the given reference triangle."""
            model = create_model('X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02487(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-02487.json"))
            write_center_svg(
                model_acute,
                here / "x-02487.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2487¶

X₂₄₈₇¶