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X₂₄₉₁¶

RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY CIRCLE}

X₂₄₉₁ = center of bicevian conic of X₅₁₁ and X₅₁₂

X₂₄₉₁ (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2491 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY 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,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02491(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2491 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY CIRCLE} on reference triangle ABC."""
            X_2491 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))*(b**(4) + c**(4) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_2491", classes=["selected", "target"])
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            X_231 = eval_trilinear_point(model, A, B, C, '(cos(B))*(4*(sin(C))**(2) - 1)*(cos(A)*sin(B) - sin(A)*cos(B)) - (cos(C))*(4*(sin(B))**(2) - 1)*(cos(C)*sin(A) - sin(C)*cos(A))', ID="X_231", classes=["center", "incident"])
            central_line(model, X_230, X_231, 230, 231, incident=True)
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_690 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))*(2*a**(2) - b**(2) - c**(2))', ID="X_690", classes=["center", "incident"])
            central_line(model, X_39, X_690, 39, 690, incident=True)
            X_351 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(b**(2) + c**(2) - 2*a**(2)))', ID="X_351", classes=["center", "incident"])
            X_865 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*(csc(C))**(2)*sin(C - A)*csc(A - B) - sin(2*C)*(csc(B))**(2)*sin(B - A)*csc(A - C))', ID="X_865", classes=["center", "incident"])
            central_line(model, X_351, X_865, 351, 865, incident=True)
            return promote_point_to_top(model, X_2491)


        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_2491 on the given reference triangle."""
            model = create_model('X_2491 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY CIRCLE}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02491(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-02491.json"))
            write_center_svg(
                model_acute,
                here / "x-02491.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2491¶

X₂₄₉₁¶