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X₃₄₂₃¶

X₁-VERTEX CONJUGATE OF X₅₇

X₃₄₂₃ (X₁-VERTEX CONJUGATE OF X₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3423 = X_1-VERTEX CONJUGATE OF X_57."""

        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,
            gergonne_point_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03423(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3423 = X_1-VERTEX CONJUGATE OF X_57 on reference triangle ABC."""
            X_2550 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c + a*cos(B)*cos(C)))', ID="X_2550", classes=["center"])
            X_3423 = isogonal_conjugate(model, A, B, C, X_2550, ID="X_3423", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center", "incident"])
            central_line(model, X_3, X_41, 3, 41, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            central_line(model, X_25, X_57, 25, 57, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            central_line(model, X_7, X_105, 7, 105, incident=True)
            return promote_point_to_top(model, X_3423)


        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_3423 on the given reference triangle."""
            model = create_model('X_3423 = X_1-VERTEX CONJUGATE OF X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03423(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-03423.json"))
            write_center_svg(
                model_acute,
                here / "x-03423.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3423¶

X₃₄₂₃¶