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X₁₀₉₈¶

TRILINEAR SQUARE OF X₂₁

X₁₀₉₈ (TRILINEAR SQUARE OF X₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1098 = TRILINEAR SQUARE OF X_21."""

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


        def construct_x_01098(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1098 = TRILINEAR SQUARE OF X_21 on reference triangle ABC."""
            X_1098 = eval_trilinear_point(model, A, B, C, '(1/(cos(B) + cos(C))**(2))', ID="X_1098", classes=["selected", "target"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_21, X_60, 21, 60, incident=True)
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            central_line(model, X_58, X_86, 58, 86, incident=True)
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_270 = eval_trilinear_point(model, A, B, C, '(sec(A))/(1 + cos(B - C))', ID="X_270", classes=["center", "incident"])
            central_line(model, X_29, X_270, 29, 270, incident=True)
            return promote_point_to_top(model, X_1098)


        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_1098 on the given reference triangle."""
            model = create_model('X_1098 = TRILINEAR SQUARE OF X_21')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01098(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-01098.json"))
            write_center_svg(
                model_acute,
                here / "x-01098.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1098¶

X₁₀₉₈¶