For a moving point P on $x^2 + y^2 = 4$ tangents PA and PB are drawn to $x^2 + y^2 = a^2$ then the locus of circumcentre of$∆PAB is \left( \left|a \right| <2\right)$

$$\begin{gathered} {\mathrm{x}}^2+{\mathrm{y}}^2=2^2 \\ Let \mathrm{P}=(2\mathrm{cos\theta }, 2s\mathrm{in\theta }) be any point on above circle \\ \mathrm{circum} \mathrm{centre} \mathrm{of} \mathrm{triangle} \mathrm{PAB} \mathrm{is} \mathrm{the} \\ \mathrm{mid}-\mathrm{point} (0,0) \mathrm{and} P \\ i.e (\mathrm{x},\mathrm{y})=(\cos \mathrm{\theta }, \sin \mathrm{\theta }) \\ \Rightarrow x=\cos \theta ,y=\sin \theta \\ Locus of centre of circum circle is x^2+y^2={\cos }^2\theta +{\sin }^2\theta =1 \\ \Rightarrow {\mathrm{x}}^2+{\mathrm{y}}^2=1 \end{gathered}$$