The centre and radius of given circle x2+y2−2x−4y−20=0 is C1(1,2) and r=√12+22+20=5 since, the radii of the two circles are equal. therefore the two circles will touch externally and the point of contact will be the mid-point between two centres. Let coordinate of the centre of required circle be(h,k) ∴‌‌‌
h+1
2
=5 and ‌
k+2
2
=5 ⇒‌‌h=9 and k=8 Hence, the centre is (9,8)