← etc / Encyclopedia of Triangle Centers

X₃₄₉₇¶

ISOGONAL CONJUGATE OF X₃₄₉₆

X₃₄₉₇ is the isogonal conjugate of X₃₄₉₆.

X₃₄₉₇ (ISOGONAL CONJUGATE OF X₃₄₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3497 = ISOGONAL CONJUGATE OF X_3496."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03497(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3497 = ISOGONAL CONJUGATE OF X_3496 on reference triangle ABC."""
            X_3496 = eval_trilinear_point(model, A, B, C, '(b**(3) + c**(3) - a**(3) + a*b*c)', ID="X_3496", classes=["center"])
            X_3497 = isogonal_conjugate(model, A, B, C, X_3496, ID="X_3497", classes=["selected", "target"])
            X_257 = eval_trilinear_point(model, A, B, C, '1/(a**(3) + a*b*c)', ID="X_257", classes=["center", "incident"])
            X_384 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) + b**(2)*c**(2))', ID="X_384", classes=["center", "incident"])
            central_line(model, X_257, X_384, 257, 384, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_984 = eval_trilinear_point(model, A, B, C, 'b**(2) + b*c + c**(2)', ID="X_984", classes=["center", "incident"])
            central_line(model, X_3, X_984, 3, 984, incident=True)
            X_607 = eval_trilinear_point(model, A, B, C, 'a*(1 + sec(A))', ID="X_607", classes=["center", "incident"])
            X_2221 = point_from_barycentrics(model, A, B, C, 0.20882469, 0.32409591, 0.4670794, ID="X_2221", classes=["center", "incident"])
            central_line(model, X_607, X_2221, 607, 2221, incident=True)
            return promote_point_to_top(model, X_3497)


        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_3497 on the given reference triangle."""
            model = create_model('X_3497 = ISOGONAL CONJUGATE OF X_3496')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03497(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-03497.json"))
            write_center_svg(
                model_acute,
                here / "x-03497.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3497¶

X₃₄₉₇¶