← etc / Encyclopedia of Triangle Centers

X₂₁₅₉¶

X₂-ISOCONJUGATE OF X₃₀

X₂₁₅₉ = barycentric product of PU(86)

X₂₁₅₉ (X₂-ISOCONJUGATE OF X₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2159 = X_2-ISOCONJUGATE OF X_30."""

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


        def construct_x_02159(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2159 = X_2-ISOCONJUGATE OF X_30 on reference triangle ABC."""
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center"])
            central_line(model, X_71, X_74, 71, 74)
            central_line(model, X_48, X_163, 48, 163)
            X_2159 = intersect_lines(model, X_71, X_74, X_48, X_163, ID="X_2159", classes=["selected", "target"])
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            central_line(model, X_63, X_662, 63, 662, incident=True)
            return promote_point_to_top(model, X_2159)


        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_2159 on the given reference triangle."""
            model = create_model('X_2159 = X_2-ISOCONJUGATE OF X_30')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02159(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-02159.json"))
            write_center_svg(
                model_acute,
                here / "x-02159.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2159¶

X₂₁₅₉¶