Radii of 2 circles are 10 cm and 4 cm respectively. Find the distance between their centres if they touch internally.
[3 Marks]

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Solution

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

Radius of the bigger circle = $r_{1}$ = 10 cm

Radius of the smaller circle = $r_{2}$ = 4 cm

The 2 circles touch each other at X internally.

OX = $r_{1}$ = 10 cm

$O^{1} X = r_{2}$ = 4 cm
[1 Mark]

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

$= r_{1} - r_{2}$
= 10 - 4
= 6 cm
[1 Mark]

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