Equation of given circle x2+y2−2x−4y−20=0 ⇒(x−1)2+(y−2)2=25......(i) Having centre C1(1,2) and radius 5 units. ∵ Another circle touches the circle (i) at point (5,5) having radius 5 units, so centre ' C2 ' of the second circle is collinear with C1 and point (5,5) is the mid-point of C1C2, so C2(9,8). So, equation of the second circle is (x−9)2+(y−8)2=25 ⇒x2+y2−18x−16y+120=0