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X₁₁₁₀¶

TRILINEAR SQUARE OF X₁₀₁

X₁₁₁₀ = crosssum of X₁₁ and X₁₀₈₆

X₁₁₁₀ (TRILINEAR SQUARE OF X₁₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1110 = TRILINEAR SQUARE OF X_101."""

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


        def construct_x_01110(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1110 = TRILINEAR SQUARE OF X_101 on reference triangle ABC."""
            X_1110 = eval_trilinear_point(model, A, B, C, '((a/(b - c))**(2))', ID="X_1110", classes=["selected", "target"])
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_59 = eval_trilinear_point(model, A, B, C, '1/(1 - cos(B - C))', ID="X_59", classes=["center", "incident"])
            central_line(model, X_36, X_59, 36, 59, incident=True)
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            X_663 = eval_trilinear_point(model, A, B, C, 'a*(b - c)*(b + c - a)', ID="X_663", classes=["center", "incident"])
            central_line(model, X_101, X_663, 101, 663, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1053 = point_from_barycentrics(model, A, B, C, 0.37037037, 0.88888889, -0.25925926, ID="X_1053", classes=["center", "incident"])
            central_line(model, X_1, X_1053, 1, 1053, incident=True)
            return promote_point_to_top(model, X_1110)


        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_1110 on the given reference triangle."""
            model = create_model('X_1110 = TRILINEAR SQUARE OF X_101')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01110(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-01110.json"))
            write_center_svg(
                model_acute,
                here / "x-01110.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1110¶

X₁₁₁₀¶