← etc / Encyclopedia of Triangle Centers

X₃₃₇₃¶

SEC(A - 3π/8) POINT

X₃₃₇₃ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

X₃₃₇₃ (SEC(A - 3π/8) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3373 = SEC(A - 3π/8) 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_trilinear_point,
            isogonal_conjugate,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03373(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3373 = SEC(A - 3π/8) POINT on reference triangle ABC."""
            X_3371 = eval_trilinear_point(model, A, B, C, 'cos(A - 3*pi  /8)', ID="X_3371", classes=["center"])
            X_3373 = isogonal_conjugate(model, A, B, C, X_3371, ID="X_3373", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_371 = eval_trilinear_point(model, A, B, C, 'cos(A -  pi  /4)', ID="X_371", classes=["center", "incident"])
            central_line(model, X_5, X_371, 5, 371, incident=True)
            return promote_point_to_top(model, X_3373)


        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_3373 on the given reference triangle."""
            model = create_model('X_3373 = SEC(A - 3π/8) POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03373(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-03373.json"))
            write_center_svg(
                model_acute,
                here / "x-03373.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3373¶

X₃₃₇₃¶