← etc / Encyclopedia of Triangle Centers

X₂₈₅¶

X₅₈-CROSS CONJUGATE OF X₂₁

X₂₈₅ (X₅₈-CROSS CONJUGATE OF X₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_285 = X_58-CROSS CONJUGATE OF X_21."""

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


        def construct_x_00285(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_285 = X_58-CROSS CONJUGATE OF X_21 on reference triangle ABC."""
            X_227 = eval_trilinear_point(model, A, B, C, '((b + c)*(cos(B) + cos(C) - cos(A) - 1)*tan(A/2))', ID="X_227", classes=["center"])
            X_285 = isogonal_conjugate(model, A, B, C, X_227, ID="X_285", classes=["selected", "target"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center", "incident"])
            central_line(model, X_21, X_84, 21, 84, incident=True)
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            central_line(model, X_29, X_81, 29, 81, incident=True)
            X_271 = eval_trilinear_point(model, A, B, C, '((cot(A)*cot(A/2))/(-1 - cos(A) + cos(B) + cos(C)))', ID="X_271", classes=["center", "incident"])
            X_282 = eval_trilinear_point(model, A, B, C, '(cot(A/2))/(-1 - cos(A) + cos(B) + cos(C))', ID="X_282", classes=["center", "incident"])
            central_line(model, X_271, X_282, 271, 282, incident=True)
            return promote_point_to_top(model, X_285)


        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_285 on the given reference triangle."""
            model = create_model('X_285 = X_58-CROSS CONJUGATE OF X_21')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00285(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-00285.json"))
            write_center_svg(
                model_acute,
                here / "x-00285.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X285¶

X₂₈₅¶