TS EAMCET 19-July-2022 Shift 2 Solved Paper

Given, two equation of circles
x2+y2−16x−20y+164=r2
and x2+y2−8x−14y+29=0
Here, C1(8,10),r1=√64+100−164+r2=r and C2(4,7),r2=√16+49−29=6
If two circles with centre C1 and C2 and radius r1 and r2, respectively intersect at two points, then
‌|r1−r2|<C1C2<r1+r2
‌|r−6|<5<r+6
When r>6, then r−6<5 and r+6>5
r<11‌ and ‌r>1
∴ The maximum integral value of r=10 When r<6, then
6−r<5,‌‌r+6>5
6−5<r,r>11
1<r.
∴r is not possible in this case.
∴ The maximum integral value of r is 10 .