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X₁₆₆₇¶

2nd INTERSECTION OF BROCARD AXIS AND 2nd LEMOINE CIRCLE

X₁₆₆₇ = reflection of X₁₆₆₆ in X₆

X₁₆₆₇ (2nd INTERSECTION OF BROCARD AXIS AND 2nd LEMOINE CIRCLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1667 = 2nd INTERSECTION OF BROCARD AXIS AND 2nd LEMOINE CIRCLE."""

        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,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01667(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1667 = 2nd INTERSECTION OF BROCARD AXIS AND 2nd LEMOINE CIRCLE on reference triangle ABC."""
            X_1666 = eval_trilinear_point(model, A, B, C, '(cos(A +  omega  ) + e*sin(A))', ID="X_1666", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_1667 = reflection_in_point(model, X_1666, X_6, ID="X_1667", classes=["selected", "target"], guide=False)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center", "incident"])
            X_2039 = eval_trilinear_point(model, A, B, C, 'e*cos(A) + 2*e*cos(B)*cos(C) + cos(A +  omega  )', ID="X_2039", classes=["center", "incident"])
            central_line(model, X_485, X_2039, 485, 2039, incident=True)
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            X_2040 = eval_trilinear_point(model, A, B, C, 'e*cos(A) + 2*e*cos(B)*cos(C) - cos(A +  omega  )', ID="X_2040", classes=["center", "incident"])
            central_line(model, X_486, X_2040, 486, 2040, incident=True)
            return promote_point_to_top(model, X_1667)


        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_1667 on the given reference triangle."""
            model = create_model('X_1667 = 2nd INTERSECTION OF BROCARD AXIS AND 2nd LEMOINE CIRCLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01667(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-01667.json"))
            write_center_svg(
                model_acute,
                here / "x-01667.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1667¶

X₁₆₆₇¶