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X₂₄₅₁¶

INVERSE-IN-2nd-LEMOINE-CIRCLE OF X₁₃₁₆

X₂₄₅₁ = inverse-in-2nd-Lemoine-circle of X₁₃₁₆

X₂₄₅₁ (INVERSE-IN-2nd-LEMOINE-CIRCLE OF X₁₃₁₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2451 = INVERSE-IN-2nd-LEMOINE-CIRCLE OF X_1316."""

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


        def construct_x_02451(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2451 = INVERSE-IN-2nd-LEMOINE-CIRCLE OF X_1316 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center"])
            X_2451 = crosspoint(model, A, B, C, X_6, X_648, ID="X_2451", classes=["selected", "target"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_6, X_523, 6, 523, incident=True)
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center", "incident"])
            X_657 = eval_trilinear_point(model, A, B, C, '(1 + cos(A))*(cos(B) - cos(C))', ID="X_657", classes=["center", "incident"])
            central_line(model, X_647, X_657, 647, 657, incident=True)
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_1570 = eval_trilinear_point(model, A, B, C, 'a*(cot(A) + cot(omega)  - 4*tan(omega)  )', ID="X_1570", classes=["center", "incident"])
            central_line(model, X_512, X_1570, 512, 1570, incident=True)
            return promote_point_to_top(model, X_2451)


        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_2451 on the given reference triangle."""
            model = create_model('X_2451 = INVERSE-IN-2nd-LEMOINE-CIRCLE OF X_1316')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02451(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-02451.json"))
            write_center_svg(
                model_acute,
                here / "x-02451.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2451¶

X₂₄₅₁¶