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X₃₉₇₈¶

X₆₉₄com[INVERSE(n(1st BROCARD TRIANGLE))]

X₃₉₇₈ = complement of Steiner-circumellipse-inverse of X₃₉

X₃₉₇₈ (X₆₉₄com[INVERSE(n(1st BROCARD TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3978 = X_694com[INVERSE(n(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_trilinear_point,
            isotomic_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03978(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3978 = X_694com[INVERSE(n(1st BROCARD TRIANGLE))] on reference triangle ABC."""
            X_694 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) - b**(2)*c**(2))', ID="X_694", classes=["center"])
            X_3978 = isotomic_conjugate(model, A, B, C, X_694, ID="X_3978", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center", "incident"])
            central_line(model, X_75, X_256, 75, 256, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_99, X_237, 99, 237, incident=True)
            return promote_point_to_top(model, X_3978)


        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_3978 on the given reference triangle."""
            model = create_model('X_3978 = X_694com[INVERSE(n(1st BROCARD TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03978(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-03978.json"))
            write_center_svg(
                model_acute,
                here / "x-03978.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3978¶

X₃₉₇₈¶