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X₃₈₄₉¶

X₅₂₄com(5th EULER TRIANGLE)

X₃₈₄₉ = infinite point of Brocard axis of the 3rd pedal triangle of X₆

X₃₈₄₉ (X₅₂₄com(5th EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3849 = X_524com(5th EULER TRIANGLE)."""

        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_03849(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3849 = X_524com(5th EULER TRIANGLE) on reference triangle ABC."""
            X_3849 = eval_barycentric_point(model, A, B, C, '(4*a**(4) - 2*b**(4) - 2*c**(4) - a**(2)*b**(2) - a**(2)*c**(2) + 2*b**(2)*c**(2))', ID="X_3849", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            central_line(model, X_2, X_187, 2, 187, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_385 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - b**(2)*c**(2))', ID="X_385", classes=["center", "incident"])
            X_671 = eval_trilinear_point(model, A, B, C, '1/(a*(2*a**(2) - b**(2) - c**(2)))', ID="X_671", classes=["center", "incident"])
            central_line(model, X_385, X_671, 385, 671, incident=True)
            return promote_point_to_top(model, X_3849)


        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_3849 on the given reference triangle."""
            model = create_model('X_3849 = X_524com(5th EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03849(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-03849.json"))
            write_center_svg(
                model_acute,
                here / "x-03849.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3849¶

X₃₈₄₉¶