Given circle, s1:x2+y2−8x−6y+21=0 and S2:x2+y2−2y−15=0 Circle S1: Centre C1(4,3), radius r1=√16+9−21=2 S2: Centre C2(0,1), radius r2=√1+15=4 Now C1C2=√42+22=√20 ∴C1C2<r1+r2⇒ circle C1 and C2 put with other.
Let point of intersection of tangent on the circle S1 and S2 is P. Now, point P divide line joining C2C1 in the ratio of their radii externally ∴