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X₃₄₄₁¶

X₁₆-VERTEX CONJUGATE OF X₁₆

X₃₄₄₁ (X₁₆-VERTEX CONJUGATE OF X₁₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3441 = X_16-VERTEX 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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03441(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3441 = X_16-VERTEX CONJUGATE OF X_16 on reference triangle ABC."""
            X_617 = point_from_barycentrics(model, A, B, C, 0.67910401, -1.0602234, 1.3811194, ID="X_617", classes=["center"])
            X_3441 = isogonal_conjugate(model, A, B, C, X_617, ID="X_3441", 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_299 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*sin(A -  pi  /3)', ID="X_299", classes=["center", "incident"])
            central_line(model, X_30, X_299, 30, 299, incident=True)
            X_16 = eval_trilinear_point(model, A, B, C, 'sin(A-  pi  /3)', ID="X_16", classes=["center", "incident"])
            X_1495 = eval_trilinear_point(model, A, B, C, 'a*((b**(2) - c**(2))**(2) + a**(2)*(b**(2) + c**(2) - 2*a**(2)))', ID="X_1495", classes=["center", "incident"])
            central_line(model, X_16, X_1495, 16, 1495, incident=True)
            X_399 = eval_trilinear_point(model, A, B, C, '5*cos(A) - 4*cos(B)*cos(C) - 8*sin(B)*sin(C)*(cos(A))**(2)', ID="X_399", classes=["center", "incident"])
            X_1337 = eval_barycentric_point(model, A, B, C, '(a**(2)*(2*D*U - 3**(1/2)*V*W)/(4*D + 3**(1/2)*a**(2)))', ID="X_1337", classes=["center", "incident"])
            central_line(model, X_399, X_1337, 399, 1337, incident=True)
            return promote_point_to_top(model, X_3441)


        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_3441 on the given reference triangle."""
            model = create_model('X_3441 = X_16-VERTEX CONJUGATE OF X_16')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03441(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-03441.json"))
            write_center_svg(
                model_acute,
                here / "x-03441.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3441¶

X₃₄₄₁¶