← etc / Encyclopedia of Triangle Centers

X₂₉₂₆¶

TANGENTIAL-ISOGONAL CONJUGATE OF X₁₆

X₂₉₂₆ is the tangential-isogonal conjugate of X₁₆.

X₂₉₂₆ (TANGENTIAL-ISOGONAL CONJUGATE OF X₁₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2926 = TANGENTIAL-ISOGONAL CONJUGATE OF X_16."""

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


        def construct_x_02926(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2926 = TANGENTIAL-ISOGONAL CONJUGATE OF X_16 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_14 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /3)', ID="X_14", classes=["center"])
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center"])
            X_1606 = point_from_barycentrics(model, A, B, C, 0.46878519, 1.3979153, -0.86670046, ID="X_1606", classes=["center"])
            central_line(model, X_3, X_14, 3, 14)
            central_line(model, X_22, X_1606, 22, 1606)
            X_2926 = intersect_lines(model, X_3, X_14, X_22, X_1606, ID="X_2926", classes=["selected", "target"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_1605 = point_from_barycentrics(model, A, B, C, 0.24200161, 0.21576869, 0.54222969, ID="X_1605", classes=["center", "incident"])
            central_line(model, X_99, X_1605, 99, 1605, incident=True)
            return promote_point_to_top(model, X_2926)


        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_2926 on the given reference triangle."""
            model = create_model('X_2926 = TANGENTIAL-ISOGONAL CONJUGATE OF X_16')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02926(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-02926.json"))
            write_center_svg(
                model_acute,
                here / "x-02926.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2926¶

X₂₉₂₆¶