Warm-up Problems

Problem 19   The radical axis of two intersecting circles passes through their points of intersection.

Problem 20   The radical axes of three circles intersect in one point, provided their centers do not lie on a line.

Problem 21   Given two circles $k_1$ and $k_2$, find the geometric place the centers of the circles $k$ perpendicular to both $k_1$ and $k_2$.