Question 165 of 219MediumMCQ
If the two circles (x−1)2+(y−3)2=r2 and x2+y2−8x+2y+8=0 intersect in two distinct points, then: Solutions · 1
Official solution
\[\left| {{r_1} - {r_2}} \right| < {C_1}{C_2}\] for intersection
\[ \Rightarrow r - 3 < 5 \Rightarrow r < 8\,\,\,\,\,\,\,\,\,...\left( 1 \right)\]
and \[{r_1} + {r_2} > {C_1}{C_2},\,\]
\[r + 3 > 5 \Rightarrow r > 2\,\,\,...\left( 2 \right)\]
From \[\left( 1 \right)\] and \[\left( 2 \right),\] 2<r<8. Answer the question to unlock