在平面上，$\stackrel{\rightharpoonup }{A{B}_1}\perp \stackrel{\rightharpoonup }{A{B}_2},\left|\stackrel{\rightharpoonup }{O{B}_1}\right|=\left|\stackrel{\rightharpoonup }{O{B}_2}\right|=1,\stackrel{\rightharpoonup }{AP}=\stackrel{\rightharpoonup }{A{B}_1}+\stackrel{\rightharpoonup }{A{B}_2}$.若$\left|\stackrel{\rightharpoonup }{OA}\right|＜\frac{1}{2}$,则$\left|\stackrel{\rightharpoonup }{OA}\right|$的取值范围是

$(0,\frac{\sqrt{5}}{2}]$ $(\frac{\sqrt{5}}{2},\frac{\sqrt{7}}{2}]$ $(\frac{\sqrt{5}}{2},\sqrt{2}]$ $(\frac{\sqrt{7}}{2},\sqrt{2}]$