← etc / Encyclopedia of Triangle Centers

X₂₃₅₅¶

X₂-ISOCONJUGATE OF X₁₇₉₆

X₂₃₅₅ (X₂-ISOCONJUGATE OF X₁₇₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2355 = X_2-ISOCONJUGATE OF X_1796."""

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


        def construct_x_02355(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2355 = X_2-ISOCONJUGATE OF X_1796 on reference triangle ABC."""
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center"])
            X_28 = eval_trilinear_point(model, A, B, C, '(tan(A))/(b + c)', ID="X_28", classes=["center"])
            X_2355 = crosspoint(model, A, B, C, X_19, X_28, ID="X_2355", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_19, X_25, 19, 25, incident=True)
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_28, X_60, 28, 60, incident=True)
            X_27 = eval_trilinear_point(model, A, B, C, '(sec(A))/(b + c)', ID="X_27", classes=["center", "incident"])
            X_242 = eval_trilinear_point(model, A, B, C, '((sec(A))*((sin(A))**(2) - sin(B)*sin(C)))', ID="X_242", classes=["center", "incident"])
            central_line(model, X_27, X_242, 27, 242, incident=True)
            return promote_point_to_top(model, X_2355)


        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_2355 on the given reference triangle."""
            model = create_model('X_2355 = X_2-ISOCONJUGATE OF X_1796')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02355(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-02355.json"))
            write_center_svg(
                model_acute,
                here / "x-02355.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2355¶

X₂₃₅₅¶