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X₃₄₂₄¶

X₂-VERTEX CONJUGATE OF X₃

X₃₄₂₄ (X₂-VERTEX CONJUGATE OF X₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3424 = X_2-VERTEX CONJUGATE OF X_3."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03424(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3424 = X_2-VERTEX CONJUGATE OF X_3 on reference triangle ABC."""
            X_1350 = eval_trilinear_point(model, A, B, C, 'a - 4*R*cot(omega)*cos(A)', ID="X_1350", classes=["center"])
            X_3424 = isogonal_conjugate(model, A, B, C, X_1350, ID="X_3424", classes=["selected", "target"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_20, X_76, 20, 76, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_154 = eval_trilinear_point(model, A, B, C, '(cos(A) - cos(B)*cos(C))*a**(2)', ID="X_154", classes=["center", "incident"])
            central_line(model, X_2, X_154, 2, 154, incident=True)
            X_253 = eval_trilinear_point(model, A, B, C, '((csc(A))/(tan(B) + tan(C) - tan(A)))', ID="X_253", classes=["center", "incident"])
            X_1297 = eval_trilinear_point(model, A, B, C, '(a/(b**(6) + c**(6) - 2*a**(6) + a**(4)*b**(2) + a**(4)*c**(2) - b**(4)*c**(2) - b**(2)*c**(4)))', ID="X_1297", classes=["center", "incident"])
            central_line(model, X_253, X_1297, 253, 1297, incident=True)
            return promote_point_to_top(model, X_3424)


        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_3424 on the given reference triangle."""
            model = create_model('X_3424 = X_2-VERTEX CONJUGATE OF X_3')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03424(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-03424.json"))
            write_center_svg(
                model_acute,
                here / "x-03424.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3424¶

X₃₄₂₄¶