← etc / Encyclopedia of Triangle Centers

X₂₅₈₅¶

X₄-ISOCONJUGATE OF X₁₁₁₄

X₂₅₈₅ (X₄-ISOCONJUGATE OF X₁₁₁₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2585 = X_4-ISOCONJUGATE OF X_1114."""

        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,
            incenter_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02585(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2585 = X_4-ISOCONJUGATE OF X_1114 on reference triangle ABC."""
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center"])
            X_656 = eval_trilinear_point(model, A, B, C, 'tan(B) - tan(C)', ID="X_656", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2583 = point_from_barycentrics(model, A, B, C, 1.9530118, 3.0939764, -4.0469882, ID="X_2583", classes=["center"])
            central_line(model, X_521, X_656, 521, 656)
            central_line(model, X_1, X_2583, 1, 2583)
            X_2585 = intersect_lines(model, X_521, X_656, X_1, X_2583, ID="X_2585", classes=["selected", "target"])
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            X_2579 = point_from_barycentrics(model, A, B, C, -1.2817064, -2.9239046, 5.205611, ID="X_2579", classes=["center", "incident"])
            central_line(model, X_48, X_2579, 48, 2579, incident=True)
            return promote_point_to_top(model, X_2585)


        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_2585 on the given reference triangle."""
            model = create_model('X_2585 = X_4-ISOCONJUGATE OF X_1114')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02585(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-02585.json"))
            write_center_svg(
                model_acute,
                here / "x-02585.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2585¶

X₂₅₈₅¶