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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