Question 73
We are given two circles $k_1(S_1, r_1)$ and $k_2(S_2, r_2)$ in the plane, with $|S_1S_2| \gt r_1 + r_2$. Find the locus of points $X$ which do not lie on the line $S_1S_2$ and possess the following property: The segments $S_1X$ and $S_2X$ intersect successively the circles $k_1$ and $k_2$ in such points whose distances to the line $S_1S_2$ are the same. (Jaromír Šimša)