Question : In a circle, a 14 cm long chord is 24 cm from the centre of the circle. Find the length of the radius of the circle.
Option 1: 30 cm
Option 2: 25 cm
Option 3: 50 cm
Option 4: 27 cm
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Correct Answer: 25 cm
Solution :
Let O be the centre, AB be the chord, and OD $\perp $ AB.
AB = 14 cm therefore, AD = 7 cm
OD = 24 cm
$\triangle$ OAD is a right-angled triangle, by using Pythagoras theorem,
OA
2
= OD
2
+ AD
2
⇒ OA
2
= (24)
2
+ (7)
2
⇒ OA
2
= 625
⇒ OA = 25 cm
Hence, the correct answer is 25 cm.
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