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X₁₁₁₁¶

TRILINEAR SQUARE OF X₅₁₄

Let A₇B₇C₇ and A₈B₈C₈ be the Gemini triangles 7 and 8. Let A' be the trilinear product A₇*A₈ and define B' and C' cyclically. The lines AA', BB', CC' concur in X₁₁₁₁. (Randy Hutson, November 30, 2018)

X₁₁₁₁ (TRILINEAR SQUARE OF X₅₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1111 = TRILINEAR SQUARE OF X_514."""

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


        def construct_x_01111(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1111 = TRILINEAR SQUARE OF X_514 on reference triangle ABC."""
            X_1110 = eval_trilinear_point(model, A, B, C, '((a/(b - c))**(2))', ID="X_1110", classes=["center"])
            X_1111 = isogonal_conjugate(model, A, B, C, X_1110, ID="X_1111", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", 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_1, X_85, 1, 85, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_7, X_80, 7, 80, incident=True)
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_334 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(a**(2) - b*c)', ID="X_334", classes=["center", "incident"])
            central_line(model, X_76, X_334, 76, 334, incident=True)
            return promote_point_to_top(model, X_1111)


        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_1111 on the given reference triangle."""
            model = create_model('X_1111 = TRILINEAR SQUARE OF X_514')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01111(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-01111.json"))
            write_center_svg(
                model_acute,
                here / "x-01111.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1111¶

X₁₁₁₁¶