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X₁₇₀¶

X₉-ALEPH CONJUGATE OF X₉

X₁₇₀ (X₉-ALEPH CONJUGATE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_170 = X_9-ALEPH CONJUGATE OF X_9."""

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


        def construct_x_00170(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_170 = X_9-ALEPH CONJUGATE OF X_9 on reference triangle ABC."""
            X_170 = eval_trilinear_point(model, A, B, C, '(- (tan(A/2))*(sec(A/2))**(2) + (tan(B/2))*(sec(B/2))**(2) + (tan(C/2))*(sec(C/2))**(2))', ID="X_170", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_218 = eval_trilinear_point(model, A, B, C, '((cos(A/2))**(2)*((cos(B/2))**(4) + (cos(C/2))**(4) - (cos(A/2))**(4)))', ID="X_218", classes=["center", "incident"])
            central_line(model, X_43, X_218, 43, 218, incident=True)
            return promote_point_to_top(model, X_170)


        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_170 on the given reference triangle."""
            model = create_model('X_170 = X_9-ALEPH CONJUGATE OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00170(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-00170.json"))
            write_center_svg(
                model_acute,
                here / "x-00170.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X170¶

X₁₇₀¶