QJEEM24Mab66e: JEE Main 2024 Mathematics - Class 11 JEEM24Mab66e Solution: If the circles and intersect at exactly two distinct points, then

If two circles intersect at two distinct points

$\begin{aligned}& \Rightarrow\left|\mathrm{r}_1-\mathrm{r}_2\right|<\mathrm{C}_1 \mathrm{C}_2<\mathrm{r}_1+\mathrm{r}_2 \\& |\mathrm{r}-2|<\sqrt{9+16}<\mathrm{r}+2 \\& |\mathrm{r}-2|<5 \text { and } \mathrm{r}+2>5 \\& -5<\mathrm{r}-2<5 \quad \mathrm{r}>3 ~\text{......... 2}\end{aligned}$

-3<\mathrm{r}<7\quad .... (1)

From (1) and (2)

3<\text { r }<7