Question 65

Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of the larger circle which touches the smaller circle is:

Solution

Given radii of two concentric circles are 13 cm and 5 cm

Radius of the larger circle = OA = 13 cm

Radius of the smaller circle = OD = 5 cm

From the figure,

In $$\triangle$$OAD,

OD$$^2$$ + AD$$^2$$ = OA$$^2$$

$$=$$> 5$$^2$$ + AD$$^2$$ = 13$$^2$$

$$=$$> 25 + AD$$^2$$ = 169

$$=$$> AD$$^2$$ = 144

$$=$$> AD = 12 cm

Length of the chord = 2(AD) = 2(12) = 24 cm

Hence, the correct answer is Option C

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