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X₁₀₈₈¶

TRILINEAR SQUARE OF X₇

X₁₀₈₈ is the Brianchon point (perspector) of the inellipse that is the trilinear square of the Gergonne line. The center of this inellipse is X₁₁₀₁₉. (Randy Hutson, October 15, 2018)

X₁₀₈₈ (TRILINEAR SQUARE OF X₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1088 = TRILINEAR SQUARE OF X_7."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01088(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1088 = TRILINEAR SQUARE OF X_7 on reference triangle ABC."""
            X_1088 = eval_trilinear_point(model, A, B, C, '(sec(A/2))**(4)', ID="X_1088", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_2, X_85, 2, 85, incident=True)
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            X_269 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)', ID="X_269", classes=["center", "incident"])
            central_line(model, X_86, X_269, 86, 269, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_354 = eval_trilinear_point(model, A, B, C, '(b - c)**(2) - a*b - a*c', ID="X_354", classes=["center", "incident"])
            central_line(model, X_7, X_354, 7, 354, incident=True)
            return promote_point_to_top(model, X_1088)


        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_1088 on the given reference triangle."""
            model = create_model('X_1088 = TRILINEAR SQUARE OF X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01088(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-01088.json"))
            write_center_svg(
                model_acute,
                here / "x-01088.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1088¶

X₁₀₈₈¶