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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