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X₂₉₂₁¶

TANGENTIAL-ISOGONAL CONJUGATE OF X₉

X₂₉₂₁ is the tangential-isogonal conjugate of X₉.

X₂₉₂₁ (TANGENTIAL-ISOGONAL CONJUGATE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2921 = TANGENTIAL-ISOGONAL CONJUGATE OF X_9."""

        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_02921(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2921 = TANGENTIAL-ISOGONAL CONJUGATE OF X_9 on reference triangle ABC."""
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center"])
            X_347 = eval_trilinear_point(model, A, B, C, '((-1 - cos(A) + cos(B) + cos(C))*(sec(A/2))**(2))', ID="X_347", classes=["center"])
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center"])
            X_1104 = point_from_barycentrics(model, A, B, C, 0.17229255, 0.32067511, 0.50703235, ID="X_1104", classes=["center"])
            central_line(model, X_22, X_347, 22, 347)
            central_line(model, X_36, X_1104, 36, 1104)
            X_2921 = intersect_lines(model, X_22, X_347, X_36, X_1104, ID="X_2921", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_1603 = point_from_barycentrics(model, A, B, C, 1.1738452, 1.1872659, -1.3611111, ID="X_1603", classes=["center", "incident"])
            central_line(model, X_3, X_1603, 3, 1603, incident=True)
            return promote_point_to_top(model, X_2921)


        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_2921 on the given reference triangle."""
            model = create_model('X_2921 = TANGENTIAL-ISOGONAL CONJUGATE OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02921(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-02921.json"))
            write_center_svg(
                model_acute,
                here / "x-02921.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2921¶

X₂₉₂₁¶