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Workings of radially inwards velocity vector in circular motion

My understanding of circular motion is that the resultant vector of the tangential and radial acceleration causes uniform/ non uniform circular motion depending on whether tangential acceleration is in effect with radial acceleration being a prerequisite. So for uniform circular motion where the radial acceleration brings about an inwards velocity causing a curvature in the path of the object, but if the radial acceleration is constant wouldn't the velocity keep increasing thereby eventually sending the object into a spiral and not uniform circular motion? So far I haven't seen anyone mention this other than bringing up the point that it simply curves the trajectory which is fine and well but wouldn't a constant increase in radial velocity dominate the resultant velocity vector and curve the trajectory more and more over time? I apologize if I'm missing something obvious.