← etc / Encyclopedia of Triangle Centers

X₂₂₁₅¶

X₂-ISOCONJUGATE OF X₄₀₅

X₂₂₁₅ (X₂-ISOCONJUGATE OF X₄₀₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2215 = X_2-ISOCONJUGATE OF X_405."""

        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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02215(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2215 = X_2-ISOCONJUGATE OF X_405 on reference triangle ABC."""
            X_2215 = eval_barycentric_point(model, A, B, C, 'a**(2)/(a**(3) - a*(b + c)**(2) - 2*b*c*(b + c))', ID="X_2215", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            central_line(model, X_1, X_71, 1, 71, incident=True)
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            central_line(model, X_48, X_58, 48, 58, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            central_line(model, X_63, X_86, 63, 86, incident=True)
            return promote_point_to_top(model, X_2215)


        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_2215 on the given reference triangle."""
            model = create_model('X_2215 = X_2-ISOCONJUGATE OF X_405')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02215(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-02215.json"))
            write_center_svg(
                model_acute,
                here / "x-02215.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2215¶

X₂₂₁₅¶