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X₂₁₆₀¶

X₂-ISOCONJUGATE OF X₃₅

A construction for X₂₁₆₀ appears in Dasari Naga Vijay Krishna, On the Feuerbach Triangle.

X₂₁₆₀ (X₂-ISOCONJUGATE OF X₃₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2160 = X_2-ISOCONJUGATE OF X_35."""

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


        def construct_x_02160(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2160 = X_2-ISOCONJUGATE OF X_35 on reference triangle ABC."""
            X_2160 = eval_trilinear_point(model, A, B, C, '(sin(A))/(1 + 2*cos(A))', ID="X_2160", classes=["selected", "target"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            central_line(model, X_9, X_46, 9, 46, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_199 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) - a**(4) + (b**(2) + c**(2) - a**(2))*(b*c + c*a + a*b)))', ID="X_199", classes=["center", "incident"])
            central_line(model, X_55, X_199, 55, 199, incident=True)
            X_284 = eval_trilinear_point(model, A, B, C, '(sin(A))/(cos(B) + cos(C))', ID="X_284", classes=["center", "incident"])
            X_501 = eval_trilinear_point(model, A, B, C, '(a*(a**(3) - b**(3) - c**(3) - b*c*(a + b + c) + a*b*(a - b) + a*c*(a - c))/(b + c))', ID="X_501", classes=["center", "incident"])
            central_line(model, X_284, X_501, 284, 501, incident=True)
            return promote_point_to_top(model, X_2160)


        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_2160 on the given reference triangle."""
            model = create_model('X_2160 = X_2-ISOCONJUGATE OF X_35')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02160(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-02160.json"))
            write_center_svg(
                model_acute,
                here / "x-02160.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2160¶

X₂₁₆₀¶