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X₈₂₅¶

o-(0, 3) CIRCUMCIRCLE POINT

X₈₂₅ = intersection, other than A, B, C, of circumcircle and hyperbola {A, B, C,PU(12)}}

X₈₂₅ (o-(0, 3) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_825 = o-(0, 3) CIRCUMCIRCLE POINT."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00825(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_825 = o-(0, 3) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_824 = eval_trilinear_point(model, A, B, C, '(a **(-1)*(b**(3) - c**(3)) + a**(2)*(b**(0) - c**(0)))', ID="X_824", classes=["center"])
            X_825 = isogonal_conjugate(model, A, B, C, X_824, ID="X_825", classes=["selected", "target"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center", "incident"])
            central_line(model, X_99, X_163, 99, 163, incident=True)
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center", "incident"])
            central_line(model, X_103, X_572, 103, 572, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_753 = eval_trilinear_point(model, A, B, C, '(1/(a **(-1)*(b**(3) + c**(3)) - a**(2)*(b**(0) + c**(0))))', ID="X_753", classes=["center", "incident"])
            central_line(model, X_6, X_753, 6, 753, incident=True)
            return promote_point_to_top(model, X_825)


        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_825 on the given reference triangle."""
            model = create_model('X_825 = o-(0, 3) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00825(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-00825.json"))
            write_center_svg(
                model_acute,
                here / "x-00825.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X825¶

X₈₂₅¶