I have the following representation: - line pass through the centers of the circles
I have to find the coordinates of the points of intersection of the line with circles (4 points). From these 4 points I have to choose 2 points , so that the distance between them to be minimal .
If I denote the coordinates of the center of the circle with $x_a,y_a$ (respectively ,$x_b,y_b$) and radius with $r_a$ , $(r_b)$ I have the following:
$(x+x_a)^2+(y+y_a)^2=r_a^2$ (circle A)
Computing the system with WolframAlpha I got some bulky answers.
Is there any trick to ease the solving of the system ? Thanks in advance.