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X₂₀₇₆¶

INVERSE-IN-CIRCUMCIRCLE OF X₃₉

Let T₁ be the circumcevian triangle of the 1st Brocard point, and let T₂ be the circumcevian triangle of the 2nd Brocard point. Let V_AV_BV_C be the vertex triangle of T₁ and T₂, and let \(S_{A}\)\(S_{B}\)\(S_{C}\) be the side triangle of T₁ and T₂. The lines V_A\(S_{A}\), V_B\(S_{B}\), V_C\(S_{C}\) concur in X₂₀₇₆.

X₂₀₇₆ (INVERSE-IN-CIRCUMCIRCLE OF X₃₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X_39."""

        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,
            ceva_conjugate,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02076(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X_39 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_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_2076 = ceva_conjugate(model, A, B, C, X_694, X_6, ID="X_2076", classes=["selected", "target"])
            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_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            X_384 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) + b**(2)*c**(2))', ID="X_384", classes=["center", "incident"])
            central_line(model, X_141, X_384, 141, 384, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_732 = eval_trilinear_point(model, A, B, C, '(a **(-3)*(b**(2) + c**(2)) - a**(1)*(b **(-2) + c **(-2)))', ID="X_732", classes=["center", "incident"])
            central_line(model, X_99, X_732, 99, 732, incident=True)
            return promote_point_to_top(model, X_2076)


        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_2076 on the given reference triangle."""
            model = create_model('X_2076 = INVERSE-IN-CIRCUMCIRCLE OF X_39')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02076(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-02076.json"))
            write_center_svg(
                model_acute,
                here / "x-02076.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2076¶

X₂₀₇₆¶