Question : AB is a chord in a circle of radius 13 cm. From centre O, a perpendicular is drawn through AB intersecting AB at point C. The length of OC is 5 cm. What is the length of AB?
Option 1: 24 cm
Option 2: 12 cm
Option 3: 20 cm
Option 4: 15 cm
Correct Answer: 24 cm
Solution :
As shown in the given figure,
Perpendicular drawn from the centre of a circle to the chord bisects the chord.
Therefore, AC = BC and $\angle$OCB = 90°
Thus, $\triangle$OCB is a right-angled triangle.
By Pythagoras Theorem,
$OB^2 = OC^2 + CB^2$
$⇒CB^2 = OB^2 - OC^2$
$⇒CB^2 = 13^2 - 5^2$
$⇒CB^2 = 169 - 25 = 144$
$⇒CB = \sqrt{144} = 12$
$\therefore AB = 2CB = 2 \times 12 = 24$ cm
Hence, the correct answer is 24 cm.
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