Given, circles are x2+y2=4 and x2+y2−4x+2y−4=0 i.e. ‌‌x2+y2=4 . . . (i) and (x−2)2−4+(y+1)2−1−4=0 ⇒x2+y2=4 and (x−2)2+(y+1)2=9 . . . (ii) Center and radius of circles (i) is c1=(0,0),r1=2 and center and radii of circle (ii) is c2=(2,−1),r2=3 So, difference between c1 and c2=√5 Now here, 1=r2−r1<√5=c1c2<5=r1+r2 r2−r1<c1c2<r1+r2 Hence, there will be two common tangents.