The centres of two circles of radii 3 cm and 2 cm are 8 cm apart. Find the length of the common tangent.
√39 cm
In the figure, MN is the common tangent. A and B are the centres of the two circles with radii 3 cm and 2 cm respectively.
AB=8 cm. AM=3 cm and BN=2 cm. Draw BC perpendicular to AM extended forward.
Since BCMN is a rectangle, CM=BN=2 cm.
Now, AC=AM+CM=3 cm+2 cm=5 cm.
In ABC, AB2=BC2+AC2
BC2=AB2−AC2
=82−52
BC=√39 cm