If radii of two circles are 4 cm and 2.8 cm. Draw figure of these circles touching each other - (i) externally (ii) internally.

Answer: (i) Keep the centres 6.8 cm apart; (ii) keep the centres 1.2 cm apart.

(i) Touching externally (distance between centres = 4 + 2.8 = 6.8 cm):

1. Draw seg AB of length 6.8 cm.
2. With centre A and radius 4 cm draw a circle. It cuts seg AB at a point C (AC = 4 cm, so CB = 2.8 cm).
3. With centre B and radius 2.8 cm draw a circle. It passes through C.

The two circles touch each other externally at C.

(ii) Touching internally (distance between centres = 4 − 2.8 = 1.2 cm):

1. Draw a ray PX and mark Q on it with PQ = 1.2 cm.
2. With centre P and radius 4 cm draw a circle; it cuts ray PX at T (PT = 4 cm, so QT = 2.8 cm).
3. With centre Q and radius 2.8 cm draw a circle; it passes through T.

The smaller circle lies inside the bigger one and they touch internally at T.