← etc / Encyclopedia of Triangle Centers

X₃₅₁₉¶

ISOGONAL CONJUGATE OF X₃₅₁₈

X₃₅₁₉ is the isogonal conjugate of X₃₅₁₈.

X₃₅₁₉ (ISOGONAL CONJUGATE OF X₃₅₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3519 = ISOGONAL CONJUGATE OF X_3518."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            anticomplement,
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03519(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3519 = ISOGONAL CONJUGATE OF X_3518 on reference triangle ABC."""
            X_1493 = eval_trilinear_point(model, A, B, C, '(csc(B +  pi  /6)*csc(C -  pi  /6) + csc(C +  pi  /6)*csc(B -  pi  /6))', ID="X_1493", classes=["center"])
            X_3519 = anticomplement(model, A, B, C, X_1493, ID="X_3519", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_17 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /6)', ID="X_17", classes=["center", "incident"])
            central_line(model, X_6, X_17, 6, 17, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_93 = eval_trilinear_point(model, A, B, C, 'sec(3*A)', ID="X_93", classes=["center", "incident"])
            central_line(model, X_4, X_93, 4, 93, incident=True)
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            central_line(model, X_54, X_140, 54, 140, incident=True)
            return promote_point_to_top(model, X_3519)


        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_3519 on the given reference triangle."""
            model = create_model('X_3519 = ISOGONAL CONJUGATE OF X_3518')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03519(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-03519.json"))
            write_center_svg(
                model_acute,
                here / "x-03519.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3519¶

X₃₅₁₉¶