Two concentric circles are drawn with radii 20 cm and 16 cm. What will be the length of a chord of the larger circle which is tangent to the smaller circle?
Answer & explanation
Correct answer: option 2
As BOC is an right angled triangle at C
Using Pythagoras theorem
⇒ \( { BO}^{2 } \) = \( { CO}^{2 } \) + \( { BC}^{2 } \)
⇒ \( { 20}^{2 } \) = \( { 16}^{2 } \) + \( { BC}^{2 } \)
⇒ 400 = 256 + \( { BC}^{2 } \)
⇒ BC = \(\sqrt {400\; - \; 256 }\)
⇒ BC = \(\sqrt {144}\)
⇒ BC = 12 cm
Now, as the line divides in 2 parts,
⇒ AB = 2BC = 2(12) = 24cm
Therefore, the length of the chord is 24 cm.