Paragraph: Read the following passage and answer the questions. Let $ABCD$ be a square of side length $2$ units. $C_2$ is the circle through vertices $A, B, C, D$ and $C_1$ is the circle touching all the sides of square $ABCD$. $L$ is the line through $A$.

A line $M$ through $A$ is drawn parallel to $BD$. Points $S$ moves such that its distances from the line $BD$ and the vertex $A$ are equal. If locus of $S$ cuts $M$ at $T_2$ and $T_3$ and $AC$ at $T_1$, then area of $\triangle AT_1T_2T_3$ is