Question 69

If two concentric circles are of radii 13 cm and 12 cm, respectively, then the length of the chord of the larger circle which touches the smaller circle is:

Solution

Given, radii of two concentric circles are 13cm and 12cm

From the figure,

Using Pythagoras theorem,

$$\text{OD}^2+\text{DB}^2=\text{OB}^2\ $$

$$=$$> $$12^2+\text{DB}^2=13^2\ $$

$$=$$> $$144+\text{DB}^2=169$$

$$=$$> $$\text{DB}^2=25$$

$$=$$> $$\text{DB}=5\text{cm}$$

$$\therefore\ $$Length of the chord of the larger circle which touches the smaller circle = AB = 2BD = 2(5) = 10cm

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