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X₁₁₀₆¶

TRILINEAR SQUARE OF X₅₆

X₁₁₀₆ = trilinear product of vertices of tangential mid-arc triangle

X₁₁₀₆ (TRILINEAR SQUARE OF X₅₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1106 = TRILINEAR SQUARE OF X_56."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01106(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1106 = TRILINEAR SQUARE OF X_56 on reference triangle ABC."""
            X_341 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*(b + c - a)**(2)', ID="X_341", classes=["center"])
            X_1106 = isogonal_conjugate(model, A, B, C, X_341, ID="X_1106", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            central_line(model, X_31, X_56, 31, 56, incident=True)
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_34, X_244, 34, 244, incident=True)
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", 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_36, X_255, 36, 255, incident=True)
            return promote_point_to_top(model, X_1106)


        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_1106 on the given reference triangle."""
            model = create_model('X_1106 = TRILINEAR SQUARE OF X_56')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01106(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-01106.json"))
            write_center_svg(
                model_acute,
                here / "x-01106.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1106¶

X₁₁₀₆¶