Radii of 2 circles are 16 cm and 8 cm. Find the distance between their centres if they touch internally.

8 cm

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2 cm

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4 cm

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24 cm

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Solution

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 $= O O^{1} = X O - X O^{1}$

$= r_{1} - r_{2}$
= 16 - 8
= 8 cm

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