The diagram shows the problem:
SN is the perpendicular from S on to OM. Isosceles triangles ROS and SMT are formed by the radii R1 and R2 of the two circles. Triangles OSN and MSN are half the areas of the isosceles triangles ROS and SMT respectively. You can see this if you drop perpendiculars from the vertices of the two isosceles onto RS and ST. From this RS=2ON and ST=2NM, so RS+ST=RT=2(ON+NM)=2OM=2×7=14cm.