Question

Draw a pair of direct common tangents to two circles of radii 2.5 cm whose centres are at 4 cm apart.

Answer 1

Draw a line segment $AB=4cm$

Taking $A$ and $B$ as centre draw two circles of radius $2.5cm$

Draw perpendiculars $PR$ at $A$ and $QS$ at $B$

Perpendicular at $A$ intersects circle 1 at $P$ and $R$ while perpendicular drawn at $B$ intersects circle 2 at $Q,S$.

Join $PQ$ and $RS$.

These are the required direct tangents.