← etc / Encyclopedia of Triangle Centers

X₂₉₂₈¶

TANGENTIAL-ISOGONAL CONJUGATE OF X₁₈

X₂₉₂₈ is the tangential-isogonal conjugate of X₁₈.

X₂₉₂₈ (TANGENTIAL-ISOGONAL CONJUGATE OF X₁₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2928 = TANGENTIAL-ISOGONAL CONJUGATE OF X_18."""

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


        def construct_x_02928(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2928 = TANGENTIAL-ISOGONAL CONJUGATE OF X_18 on reference triangle ABC."""
            X_2928 = point_from_barycentrics(model, A, B, C, 0.39454063, 0.47643495, 0.12902442, ID="X_2928", classes=["selected", "target"])
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            X_2937 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(8) - 2*a**(6)*(b**(2) + c**(2)) - a**(4)*b**(2)*c**(2) + a**(2)*(2*b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + 2*c**(6)) - (b**(2) - c**(2))**(2)*(b**(4) + c**(4)))', ID="X_2937", classes=["center", "incident"])
            central_line(model, X_16, X_2937, 16, 2937, incident=True)
            return promote_point_to_top(model, X_2928)


        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_2928 on the given reference triangle."""
            model = create_model('X_2928 = TANGENTIAL-ISOGONAL CONJUGATE OF X_18')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02928(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-02928.json"))
            write_center_svg(
                model_acute,
                here / "x-02928.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2928¶

X₂₉₂₈¶