Question 26
Two circles, both with the same radius $r$, are placed in the plane without intersecting each other. A line in the plane intersects the first circle at the points $A, B$ and the other at the points $C, D$ so that $|A B|=|B C|=|C D|=14~\mathrm{cm}$. Another line intersects the circles at points $E, F$ and $G, H$ respectively, so that $|E F|=|F G|=|G H|=6~\mathrm{cm}$. Find the radius $r$.