The equation of the circle having radius 5 and touching the circle x2+y2−2x−4y−20=0 at (5,5) is

The centre of the given circle is (1, 2) and its radius is 5. Since the radii of the two circles are equal. Therefore, the two circles will touch externally and the point of contact will lie mid-way between the two centres. Let the coordinates of the centre of the required circle be (h, k). Then,h+12=5 and k+22=5⇒h=9 and k=8Thus, the centre of the required circle is (9, 8). Its equation is(x−9)2+(y−8)2=52⇒x2+y2−18x−16y+120=0