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X₉₂₃¶

POINT ALBIREO

X₉₂₃ = barycentric product X₁*X₁₁₁

X₉₂₃ (POINT ALBIREO) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_923 = POINT ALBIREO."""

        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,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00923(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_923 = POINT ALBIREO on reference triangle ABC."""
            X_923 = eval_trilinear_point(model, A, B, C, '(a**(2)/(b**(2) + c**(2) - 2*a**(2)))', ID="X_923", classes=["selected", "target"])
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_42, X_101, 42, 101, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", 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_31, X_163, 31, 163, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_1, X_662, 1, 662, incident=True)
            return promote_point_to_top(model, X_923)


        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_923 on the given reference triangle."""
            model = create_model('X_923 = POINT ALBIREO')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00923(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-00923.json"))
            write_center_svg(
                model_acute,
                here / "x-00923.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X923¶

X₉₂₃¶