← etc / Encyclopedia of Triangle Centers

X₂₃₁₆¶

X₂-ISOCONJUGATE OF X₁₃₁₉

X₂₃₁₆ is the perspector of the anticevian triangle of X₁₀₆ and the unary cofactor triangle of the intangents triangle, and also the perspector of ABC and the unary cofactor triangle of Gemini triangle 9. (Randy Hutson, November 30, 2018)

X₂₃₁₆ (X₂-ISOCONJUGATE OF X₁₃₁₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2316 = X_2-ISOCONJUGATE OF X_1319."""

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


        def construct_x_02316(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2316 = X_2-ISOCONJUGATE OF X_1319 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_88 = eval_trilinear_point(model, A, B, C, '1/(b + c - 2*a)', ID="X_88", classes=["center"])
            central_line(model, X_6, X_101, 6, 101)
            central_line(model, X_57, X_88, 57, 88)
            X_2316 = intersect_lines(model, X_6, X_101, X_57, X_88, ID="X_2316", classes=["selected", "target"])
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            central_line(model, X_44, X_517, 44, 517, incident=True)
            return promote_point_to_top(model, X_2316)


        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_2316 on the given reference triangle."""
            model = create_model('X_2316 = X_2-ISOCONJUGATE OF X_1319')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02316(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-02316.json"))
            write_center_svg(
                model_acute,
                here / "x-02316.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2316¶

X₂₃₁₆¶