Question : A chord of length 24 cm is at a distance of 5 cm from the centre of the circle. The radius of the circle is:
Option 1: 13 cm
Option 2: 12 cm
Option 3: 16 cm
Option 4: 15 cm
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Correct Answer: 13 cm
Solution : Let O be the centre of the circle. Let AB be the chord of length 24 cm Let OD be perpendicular from the centre to the chord AB of length 5 cm. We know the perpendicular from the centre to a chord bisects the chord. So, AD = BD = 12 units Applying Pythagoras theorem in triangle OBD, OB 2 = OD 2 + DB 2 ⇒ OB 2 = 5 2 + 12 2 ⇒ OB 2 = 169 ⇒ OB = 13 Hence, the correct answer is 13 cm.
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