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X₂₉₇₄¶

8th MACBEATH POINT

X₂₉₇₄ = reflection of X₂₉₇₁ in X₅

X₂₉₇₄ (8th MACBEATH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2974 = 8th MACBEATH 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02974(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2974 = 8th MACBEATH POINT on reference triangle ABC."""
            X_2971 = eval_trilinear_point(model, A, B, C, '((a*(b**(2) - c**(2)))**(2)*cos(B)*cos(C))', ID="X_2971", classes=["center"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_2974 = reflection_in_point(model, X_2971, X_5, ID="X_2974", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", 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_3, X_76, 3, 76, incident=True)
            X_131 = point_from_barycentrics(model, A, B, C, 0.57236082, 0.12379803, 0.30384114, ID="X_131", classes=["center", "incident"])
            X_132 = point_from_barycentrics(model, A, B, C, 0.11002416, 0.049913231, 0.84006261, ID="X_132", classes=["center", "incident"])
            central_line(model, X_131, X_132, 131, 132, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_925 = eval_trilinear_point(model, A, B, C, '(sin(A))/(sec(2*B) - sec(2*C))', ID="X_925", classes=["center", "incident"])
            central_line(model, X_25, X_925, 25, 925, incident=True)
            return promote_point_to_top(model, X_2974)


        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_2974 on the given reference triangle."""
            model = create_model('X_2974 = 8th MACBEATH POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02974(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-02974.json"))
            write_center_svg(
                model_acute,
                here / "x-02974.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2974¶

X₂₉₇₄¶