I have having trouble to solve a revised-GRE graph math where it is very essential to find the answer with shortest amount of time.
The way I wanted to solve this math is, to find the intersection between the straight line and the circle. After doing that, I can guess some points below the intersection points, if that satisfies one of the conditions, that will be the answer. But it seems to me very time consuming.
Can you please give me any hints that would be a good way to solve it within a short amount of time?
Note that $(x-1)^2+(y-2)^2\lt 9$ represents the region inside the circle and that $(x-1)^2+(y-2)^2\gt 9$ represents the region outside the circle.
Also, note that $y\lt -x+2$ represents the region below the line and that $y\gt -x+2$ represents the region above the line.