← etc / Encyclopedia of Triangle Centers

X₁₀₀₀¶

ISOGONAL CONJUGATE OF X₉₉₉

End of PART 1

X₁₀₀₀ (ISOGONAL CONJUGATE OF X₉₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1000 = ISOGONAL CONJUGATE OF X_999."""

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


        def construct_x_01000(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1000 = ISOGONAL CONJUGATE OF X_999 on reference triangle ABC."""
            X_999 = eval_trilinear_point(model, A, B, C, '2 - cos(A)', ID="X_999", classes=["center"])
            X_1000 = isogonal_conjugate(model, A, B, C, X_999, ID="X_1000", classes=["selected", "target"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_55, X_104, 55, 104, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            central_line(model, X_21, X_145, 21, 145, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_392 = eval_trilinear_point(model, A, B, C, '(b + c)*(b**(2) + c**(2) - a**(2)) + 4*a*b*c', ID="X_392", classes=["center", "incident"])
            central_line(model, X_8, X_392, 8, 392, incident=True)
            return promote_point_to_top(model, X_1000)


        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_1000 on the given reference triangle."""
            model = create_model('X_1000 = ISOGONAL CONJUGATE OF X_999')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01000(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-01000.json"))
            write_center_svg(
                model_acute,
                here / "x-01000.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1000¶

X₁₀₀₀¶