← etc / Encyclopedia of Triangle Centers

X₉₃₉¶

ISOGONAL CONJUGATE OF X₉₃₈

X₉₃₉ (ISOGONAL CONJUGATE OF X₉₃₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_939 = ISOGONAL CONJUGATE OF X_938."""

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


        def construct_x_00939(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_939 = ISOGONAL CONJUGATE OF X_938 on reference triangle ABC."""
            X_938 = eval_trilinear_point(model, A, B, C, '(b*c*(a**(4) - 2*a**(3)*(b + c) - 4*a**(2)*b*c + (b - c)*(b**(2) - c**(2))*(2*a - b - c)))', ID="X_938", classes=["center"])
            X_939 = isogonal_conjugate(model, A, B, C, X_938, ID="X_939", classes=["selected", "target"])
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            central_line(model, X_34, X_55, 34, 55, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_212 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(A))', ID="X_212", classes=["center", "incident"])
            central_line(model, X_56, X_212, 56, 212, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_269 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)', ID="X_269", classes=["center", "incident"])
            central_line(model, X_3, X_269, 3, 269, incident=True)
            return promote_point_to_top(model, X_939)


        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_939 on the given reference triangle."""
            model = create_model('X_939 = ISOGONAL CONJUGATE OF X_938')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00939(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-00939.json"))
            write_center_svg(
                model_acute,
                here / "x-00939.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X939¶

X₉₃₉¶