← etc / Encyclopedia of Triangle Centers

X₈₇₃¶

ISOGONAL CONJUGATE OF X₈₇₂

X₈₇₃ (ISOGONAL CONJUGATE OF X₈₇₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_873 = ISOGONAL CONJUGATE OF X_872."""

        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,
            centroid_of,
            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_00873(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_873 = ISOGONAL CONJUGATE OF X_872 on reference triangle ABC."""
            X_872 = eval_trilinear_point(model, A, B, C, '(a*(b + c))**(2)', ID="X_872", classes=["center"])
            X_873 = isogonal_conjugate(model, A, B, C, X_872, ID="X_873", classes=["selected", "target"])
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_239 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - b*c)', ID="X_239", classes=["center", "incident"])
            central_line(model, X_81, X_239, 81, 239, incident=True)
            X_86 = eval_trilinear_point(model, A, B, C, 'b*c/(b + c)', ID="X_86", classes=["center", "incident"])
            X_310 = eval_trilinear_point(model, A, B, C, 'b**(3)*c**(3)/(b + c)', ID="X_310", classes=["center", "incident"])
            central_line(model, X_86, X_310, 86, 310, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_799 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)/((cos(B))**(2) - (cos(C))**(2))', ID="X_799", classes=["center", "incident"])
            central_line(model, X_2, X_799, 2, 799, incident=True)
            return promote_point_to_top(model, X_873)


        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_873 on the given reference triangle."""
            model = create_model('X_873 = ISOGONAL CONJUGATE OF X_872')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00873(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-00873.json"))
            write_center_svg(
                model_acute,
                here / "x-00873.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X873¶

X₈₇₃¶