I'll take assistance from the figure below.
O is the center of the circle, and A,B,C are the points on the circle, and are known. i.e. the x,y coordinates of these three points are known. I want to know, that for the center point O, and any other point, say a,b,c [small characters], if O and that particular point is in the same region.
To add to the assumption, let us say, AB and the other line are horizontal or vertical. i.e. parallel to the X and Y axis.
Also, what if I remove this assumption?
Thanks.
EDIT I guess, for the given assumption, I could just check if the other point (not the center) has the x and y coordinates, in range of the A B and C, towards the side of center. That is, if center has coordinate value more for A and not for B and not for C, then so should the other point? Will that be correct? What if the assumption is false?
You can just calculate which side of $AB$ the point is on. If $AB$ is horizontal, you just check the $y$ coordinate of the point. If $AB$ is not horizontal, you have the line AB as $y-y_A=\frac {y_B-y_A}{x_B-x_A}(x-x_A)$ A point is above the line if the left side is greater than the right.
The line through $C$ you check the same way. If it is vertical, just check the $x$ coordinate. If it is not, there is nothing to specify its slope and you need to fix that, but the idea is the same.