Reach for the Summit - M-S6-A2

Geometry Level 3

As shown above, line $l$ is tangent to curve $C:x^2+y^2-2x-2y+1=0$ and it intersects with y-axis at point $A$ , x-axis at point $B$ , $O$ is the origin, $|OA|>2, |OB|>2$ . Then find the minimum area for $\triangle AOB$ .

Let $S$ denote the minimum area. Submit $\lfloor 1000S \rfloor$ .

Reach for the Summit problem set - Mathematics