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X₃₇₃₄¶

X₆com(1st BROCARD TRIANGLE)

Let A'B'C' be the 1st Brocard triangle. Let A″ be the trilinear pole, with respect to A'B'C', of line BC, and define B″ and C″ cyclically. The lines A'A″, B'B″, C'C″ concur in X₃₇₃₄.

X₃₇₃₄ (X₆com(1st BROCARD TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3734 = X_6com(1st BROCARD 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_03734(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3734 = X_6com(1st BROCARD TRIANGLE) on reference triangle ABC."""
            X_3734 = eval_barycentric_point(model, A, B, C, '(a**(4) + 2*b**(2)*c**(2))', ID="X_3734", 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_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", 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_32, X_76, 32, 76, 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_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_30, X_141, 30, 141, incident=True)
            return promote_point_to_top(model, X_3734)


        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_3734 on the given reference triangle."""
            model = create_model('X_3734 = X_6com(1st BROCARD TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03734(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-03734.json"))
            write_center_svg(
                model_acute,
                here / "x-03734.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3734¶

X₃₇₃₄¶