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X₃₄₂₀¶

X₁-VERTEX CONJUGATE OF X₉

X₃₄₂₀ (X₁-VERTEX CONJUGATE OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3420 = X_1-VERTEX 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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03420(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3420 = X_1-VERTEX CONJUGATE OF X_9 on reference triangle ABC."""
            X_3420 = eval_barycentric_point(model, A, B, C, '(a**(2)/(a**(4) - 4*a*b*c*(b + c - a) - (b**(2) - c**(2))**(2)))', ID="X_3420", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_25, X_104, 25, 104, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_392 = eval_trilinear_point(model, A, B, C, '(b + c)*(b**(2) + c**(2) - a**(2)) + 4*a*b*c', ID="X_392", classes=["center", "incident"])
            central_line(model, X_3, X_392, 3, 392, incident=True)
            X_859 = eval_trilinear_point(model, A, B, C, '((sin(A) + sin(B))*sin(2*B)*sin(C - A) + (sin(A) + sin(C))*sin(2*C)*sin(B - A))', ID="X_859", classes=["center", "incident"])
            X_1444 = eval_trilinear_point(model, A, B, C, '(cot(A))/(b + c)', ID="X_1444", classes=["center", "incident"])
            central_line(model, X_859, X_1444, 859, 1444, incident=True)
            return promote_point_to_top(model, X_3420)


        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_3420 on the given reference triangle."""
            model = create_model('X_3420 = X_1-VERTEX CONJUGATE OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03420(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-03420.json"))
            write_center_svg(
                model_acute,
                here / "x-03420.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3420¶

X₃₄₂₀¶