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X₁₁₀₉¶

TRILINEAR SQUARE OF X₅₂₃

X₁₁₀₉ (TRILINEAR SQUARE OF X₅₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1109 = TRILINEAR SQUARE OF X_523."""

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


        def construct_x_01109(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1109 = TRILINEAR SQUARE OF X_523 on reference triangle ABC."""
            X_1101 = eval_trilinear_point(model, A, B, C, '((csc(B - C))**(2))', ID="X_1101", classes=["center"])
            X_1109 = isogonal_conjugate(model, A, B, C, X_1101, ID="X_1109", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_31, X_92, 31, 92, incident=True)
            X_91 = eval_trilinear_point(model, A, B, C, 'sec(2*A)', ID="X_91", classes=["center", "incident"])
            X_255 = eval_trilinear_point(model, A, B, C, '(cos(A))**(2)', ID="X_255", classes=["center", "incident"])
            central_line(model, X_91, X_255, 91, 255, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_11, X_523, 11, 523, incident=True)
            return promote_point_to_top(model, X_1109)


        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_1109 on the given reference triangle."""
            model = create_model('X_1109 = TRILINEAR SQUARE OF X_523')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01109(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-01109.json"))
            write_center_svg(
                model_acute,
                here / "x-01109.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1109¶

X₁₁₀₉¶