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X₃₅₁¶

CENTER OF THE PARRY CIRCLE

X₃₅₁ is the center of the Parry circle introduced in TCCT (Art. 8.13) as the circle that passes through X_i for I = 2, 15, 16, 23, 110, 111, 352, 353.

X₃₅₁ (CENTER OF THE PARRY CIRCLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_351 = CENTER OF THE PARRY 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00351(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_351 = CENTER OF THE PARRY CIRCLE on reference triangle ABC."""
            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=["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_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_526 = eval_trilinear_point(model, A, B, C, '(1 + 2*cos(2*A))*sin(B - C)', ID="X_526", classes=["center", "incident"])
            central_line(model, X_110, X_526, 110, 526, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_804 = eval_trilinear_point(model, A, B, C, 'a **(-3)*(b**(2) - c**(2)) + a**(1)*(b **(-2) - c **(-2))', ID="X_804", classes=["center", "incident"])
            central_line(model, X_2, X_804, 2, 804, incident=True)
            return promote_point_to_top(model, X_351)


        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_351 on the given reference triangle."""
            model = create_model('X_351 = CENTER OF THE PARRY CIRCLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00351(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-00351.json"))
            write_center_svg(
                model_acute,
                here / "x-00351.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X351¶

X₃₅₁¶