Let $\quad M=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x^2+y^2 \leq r^2\right\}$, where $\mathrm{r}>0$. Consider the geometric progression $\mathrm{a}_{\mathrm{n}}=\frac{1}{2^{\mathrm{n}-1}}, \mathrm{n}=1,2,3 \ldots$. Let $\mathrm{S}_0=0$ and, for $\mathrm{n} \geq 1$, let $\mathrm{S}_{\mathrm{n}}$ denote the sum of the first $n$ terms of this progression. For $n \geq 1$, let $C_n$ denote the circle with center ( $S_{n-1}, 0$ ) and radius $a_n$, and $D_n$ denote the circle with center ( $S_{n-1}, S_{n-1}$ ) and radius $a_n$. Consider $M$ with $\frac{1025}{513}$. Let $k$ be the number of all those circles $C_n$ that are inside $M$. Let $\ell$ be the maximum possible number of circles among these k circles such that no two circles intersect. Then