An aircraft turbine engine includes a low-pressure body and a high-pressure body, as well as means for drawing power on said low-pressure body, said means having a first shaft for drawing power, the radially inner end of said first shaft bearing a first bevel gear meshed with a first idler bevel wheel driven by the low-pressure body, the turbine engine further having a first annular bearing support which extends about an axis and is rigidly connected to a stator. The first bearing support includes a first cylindrical portion which extends coaxially with a second substantially cylindrical portion of the idler wheel, said first and second portions being guided one inside the other by bearings, and the idler wheel is driven by the low-pressure body by means of an annular damping piece which is independent of the first bearing support.