← etc / Encyclopedia of Triangle Centers

X₃₂₂₁¶

SS(a → bc) OF X₆₄₇

As the isogonal conjugate of a point on the circumcircle, X₃₂₂₁ lies on the line at infinity.

X₃₂₂₁ (SS(a → bc) OF X₆₄₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3221 = SS(a → bc) OF X_647."""

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


        def construct_x_03221(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3221 = SS(a → bc) OF X_647 on reference triangle ABC."""
            X_3221 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(c**(2)*a**(2) + a**(2)*b**(2) - b**(2)*c**(2)))', ID="X_3221", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_882 = point_from_barycentrics(model, A, B, C, 0.023590899, 1.0060979, -0.02968882, ID="X_882", classes=["center", "incident"])
            X_1843 = eval_trilinear_point(model, A, B, C, 'tan(A)*sin(A +  omega  )', ID="X_1843", classes=["center", "incident"])
            central_line(model, X_882, X_1843, 882, 1843, incident=True)
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center", "incident"])
            X_2451 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) - c**(2))*(a**(4) + 2*b**(2)*c**(2) - a**(2)*b**(2)- a**(2)*c**(2)))', ID="X_2451", classes=["center", "incident"])
            central_line(model, X_669, X_2451, 669, 2451, incident=True)
            return promote_point_to_top(model, X_3221)


        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_3221 on the given reference triangle."""
            model = create_model('X_3221 = SS(a → bc) OF X_647')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03221(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-03221.json"))
            write_center_svg(
                model_acute,
                here / "x-03221.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3221¶

X₃₂₂₁¶