Circle bisecting other the circumference of other circle.

Question

If the circle x2+y2+4x+22y+l=0 bisects the circumference of the circle x2+y2−2x+8y−m=0,then l*m is equal to

(A) 25

(B) 625

(C) 125

(D) 425

I don't know the condition when one circle intersects the circumference of other circle. So could not solve this question. Can someone help me in this question?

Answer 1

The first circle intersects the second circle at two points, and the arc length of the second circle between those two points is half the circumference of the second circle. This means that the line segment between the two points is a diameter, and includes the center of the circle.

Answer 2

I'm assuming there is something wrong with the second equation and if corrected to give an $r^2$ value of 5, then answer (B) looks to be the answer except these circles intercept at the origin $(0, 0)$ and $(3,-1)$.