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X₃₃₇₈¶

COT(A - π/4) POINT

X₃₃₇₈ and related points occupy Bernard Gibert’s Table 38. See the note at X₃₃₆₄.

X₃₃₇₈ (COT(A - π/4) POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3378 = COT(A - π/4) 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,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03378(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3378 = COT(A - π/4) POINT on reference triangle ABC."""
            X_3377 = eval_trilinear_point(model, A, B, C, '(tan(A -  pi  /4))', ID="X_3377", classes=["center"])
            X_3378 = isogonal_conjugate(model, A, B, C, X_3377, ID="X_3378", classes=["selected", "target"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_91 = eval_trilinear_point(model, A, B, C, 'sec(2*A)', ID="X_91", classes=["center", "incident"])
            central_line(model, X_19, X_91, 19, 91, incident=True)
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            central_line(model, X_46, X_486, 46, 486, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_1806 = eval_trilinear_point(model, A, B, C, '(a*(1 + cot(A/2))/(b + c))', ID="X_1806", classes=["center", "incident"])
            central_line(model, X_1, X_1806, 1, 1806, incident=True)
            return promote_point_to_top(model, X_3378)


        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_3378 on the given reference triangle."""
            model = create_model('X_3378 = COT(A - π/4) POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03378(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-03378.json"))
            write_center_svg(
                model_acute,
                here / "x-03378.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3378¶

X₃₃₇₈¶