← etc / Encyclopedia of Triangle Centers

X₂₁₀₉¶

X₂-ISOCONJUGATE OF X₂₁₀₈

X₂₁₀₉ (X₂-ISOCONJUGATE OF X₂₁₀₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2109 = X_2-ISOCONJUGATE OF X_2108."""

        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_02109(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2109 = X_2-ISOCONJUGATE OF X_2108 on reference triangle ABC."""
            X_2109 = eval_trilinear_point(model, A, B, C, '(a/((b + c)*a**(3) - (b**(2) - b*c + c**(2))*a**(2) - (b + c)*(b**(2) + c**(2))*a + b*c*(b**(2) + b*c + c**(2))))', ID="X_2109", classes=["selected", "target"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            X_1575 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2)) - b*c*(b + c)', ID="X_1575", classes=["center", "incident"])
            central_line(model, X_238, X_1575, 238, 1575, incident=True)
            X_1914 = eval_trilinear_point(model, A, B, C, '1 - a**(2)/(b*c)', ID="X_1914", classes=["center", "incident"])
            X_2112 = eval_trilinear_point(model, A, B, C, '(a*(a**(4) - b*c*a**(2) - (b**(3) + c**(3))*a + 2*b**(2)*c**(2)))', ID="X_2112", classes=["center", "incident"])
            central_line(model, X_1914, X_2112, 1914, 2112, incident=True)
            return promote_point_to_top(model, X_2109)


        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_2109 on the given reference triangle."""
            model = create_model('X_2109 = X_2-ISOCONJUGATE OF X_2108')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02109(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-02109.json"))
            write_center_svg(
                model_acute,
                here / "x-02109.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2109¶

X₂₁₀₉¶