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X₃₉₇₂¶

X₃₃₁₄com(3rd BROCARD TRIANGLE)

X₃₉₇₂ = perspector of ABC and circumsymmedial triangle of 1st Brocard triangle

X₃₉₇₂ (X₃₃₁₄com(3rd BROCARD TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3972 = X_3314com(3rd 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03972(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3972 = X_3314com(3rd BROCARD TRIANGLE) on reference triangle ABC."""
            X_3972 = eval_barycentric_point(model, A, B, C, '2*a**(4) + b**(2)*c**(2)', ID="X_3972", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_83 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) + c**(2))', ID="X_83", classes=["center", "incident"])
            central_line(model, X_3, X_83, 3, 83, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", 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_6, X_99, 6, 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)
            return promote_point_to_top(model, X_3972)


        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_3972 on the given reference triangle."""
            model = create_model('X_3972 = X_3314com(3rd BROCARD TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03972(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-03972.json"))
            write_center_svg(
                model_acute,
                here / "x-03972.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3972¶

X₃₉₇₂¶