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X₁₃₃₇¶

1st WERNAU POINT

X₁₃₃₇ is the tangential of X₁₅ on the Neuberg cubic.

X₁₃₃₇ (1st WERNAU POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1337 = 1st WERNAU POINT."""

        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,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01337(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1337 = 1st WERNAU POINT on reference triangle ABC."""
            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=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_616 = point_from_barycentrics(model, A, B, C, 0.54029552, 0.39971531, 0.059989162, ID="X_616", classes=["center", "incident"])
            central_line(model, X_4, X_616, 4, 616, incident=True)
            X_1157 = eval_trilinear_point(model, A, B, C, '4*cos(A) + cos(3*A)*sec(A)*sec(B - C)', ID="X_1157", classes=["center", "incident"])
            X_1338 = 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_1338", classes=["center", "incident"])
            central_line(model, X_1157, X_1338, 1157, 1338, incident=True)
            X_15 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /3)', ID="X_15", classes=["center", "incident"])
            X_2981 = eval_trilinear_point(model, A, B, C, '1/(cos(B - C) + 2*cos(A -  pi  /3))', ID="X_2981", classes=["center", "incident"])
            central_line(model, X_15, X_2981, 15, 2981, incident=True)
            return promote_point_to_top(model, X_1337)


        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_1337 on the given reference triangle."""
            model = create_model('X_1337 = 1st WERNAU POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01337(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-01337.json"))
            write_center_svg(
                model_acute,
                here / "x-01337.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1337¶

X₁₃₃₇¶