← etc / Encyclopedia of Triangle Centers

X₂₂₇₉¶

X₂-ISOCONJUGATE OF X₁₀₀₁

X₂₂₇₉ (X₂-ISOCONJUGATE OF X₁₀₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2279 = X_2-ISOCONJUGATE OF X_1001."""

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


        def construct_x_02279(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2279 = X_2-ISOCONJUGATE OF X_1001 on reference triangle ABC."""
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center"])
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center"])
            central_line(model, X_9, X_86, 9, 86)
            central_line(model, X_41, X_58, 41, 58)
            X_2279 = intersect_lines(model, X_9, X_86, X_41, X_58, ID="X_2279", classes=["selected", "target"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_213 = eval_trilinear_point(model, A, B, C, '(b + c)*a**(2)', ID="X_213", classes=["center", "incident"])
            central_line(model, X_56, X_213, 56, 213, incident=True)
            return promote_point_to_top(model, X_2279)


        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_2279 on the given reference triangle."""
            model = create_model('X_2279 = X_2-ISOCONJUGATE OF X_1001')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02279(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-02279.json"))
            write_center_svg(
                model_acute,
                here / "x-02279.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2279¶

X₂₂₇₉¶