rr =(1-Cos[tt](1-2x)/(3-2x))

PolarPlot[{rr/.x->0.5,rr/.x->0.65,rr/.x->0.8,rr/.x->0.9,rr/.x->0.99},{tt,0,2Pi},Axes->False, PlotStyle->{{Blue,Thickness[0.01]}, {Cyan, Thickness[0.01]}, {Green,Thickness[0.01]},{Orange,Thickness[0.01]}, {Red,Thickness[0.01]}}]