Question

Radii of 2 circles are 6 cm and 8 cm. Find the distance between their centres if they touch internally.

• A. 8 cm
• B. 2 cm
• C. 4 cm
• D. 24 cm

Answer 1

The correct option is A

8 cm

Consider 2 circles, one with centre 'O', and another with 'O${}^1$'.

Radius of the bigger circle = $r_1$ = 16 cm

Radius of the smaller circle = $r_2$ = 8 cm

The 2 circles touch each other at X internally.

OX = $r_1$ = 16 cm

$O^{1}X=r_2$ = 8 cm

Distance between their centres $=O{O}^1=XO-X{O}^1$

$=r_1-r_2$
= 16 - 8
= 8 cm