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X₅₄₃¶

DIRECTION OF VECTOR AX + BX + CX, where X = X₉₉

X₅₄₃ = X₅₂₄-of-1st-Brocard-triangle

X₅₄₃ (DIRECTION OF VECTOR AX + BX + CX, where X = X₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X_99."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00543(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X_99 on reference triangle ABC."""
            X_543 = eval_barycentric_point(model, A, B, C, '2*a**(4) - b**(4) - c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2) + 4*b**(2)*c**(2)', ID="X_543", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_2, X_99, 2, 99, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_376 = eval_trilinear_point(model, A, B, C, '5*cos(A) - cos(B - C)', ID="X_376", classes=["center", "incident"])
            central_line(model, X_98, X_376, 98, 376, incident=True)
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center", "incident"])
            central_line(model, X_114, X_381, 114, 381, incident=True)
            return promote_point_to_top(model, X_543)


        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_543 on the given reference triangle."""
            model = create_model('X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X_99')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00543(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-00543.json"))
            write_center_svg(
                model_acute,
                here / "x-00543.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X543¶

X₅₄₃¶