← etc / Encyclopedia of Triangle Centers

X₂₉₅₂¶

EXCENTRAL-ISOGONAL CONJUGATE OF X₆₁

X₂₉₅₂ is the excentral-isogonal conjugate of X₆₁.

X₂₉₅₂ (EXCENTRAL-ISOGONAL CONJUGATE OF X₆₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2952 = EXCENTRAL-ISOGONAL CONJUGATE OF X_61."""

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


        def construct_x_02952(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2952 = EXCENTRAL-ISOGONAL CONJUGATE OF X_61 on reference triangle ABC."""
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center"])
            X_1276 = eval_trilinear_point(model, A, B, C, '(sqrt(3/4) + sin(A +  pi  /3) - sin(B +  pi  /3) - sin(C +  pi  /3))', ID="X_1276", classes=["center"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center"])
            X_2946 = point_from_barycentrics(model, A, B, C, 0.53341416, -1.1810868, 1.6476727, ID="X_2946", classes=["center"])
            central_line(model, X_191, X_1276, 191, 1276)
            central_line(model, X_40, X_2946, 40, 2946)
            X_2952 = intersect_lines(model, X_191, X_1276, X_40, X_2946, ID="X_2952", classes=["selected", "target"])
            X_1761 = point_from_barycentrics(model, A, B, C, 0.54015296, 0.3957935, 0.064053537, ID="X_1761", classes=["center", "incident"])
            X_2321 = point_from_barycentrics(model, A, B, C, 0.47272727, 0.32727273, 0.2, ID="X_2321", classes=["center", "incident"])
            central_line(model, X_1761, X_2321, 1761, 2321, incident=True)
            return promote_point_to_top(model, X_2952)


        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_2952 on the given reference triangle."""
            model = create_model('X_2952 = EXCENTRAL-ISOGONAL CONJUGATE OF X_61')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02952(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-02952.json"))
            write_center_svg(
                model_acute,
                here / "x-02952.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2952¶

X₂₉₅₂¶