Question : The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
Option 1: 10 cm
Option 2: 13 cm
Option 3: 12 cm
Option 4: 24 cm
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Correct Answer: 13 cm
Solution :
AB = 24 cm
And OC = 5 cm
We have to find AO.
C is the middle point of the chord.
$\therefore$ AC = $\frac{24}{2} = 12\ \mathrm{cm}$
Using Pythagoras theorem,
$\text{AO}^2 = \text{AC}^2 + \text{OC}^2$
⇒ $\text{AO}^2 = 12^2 + 5^2$
⇒ $\text{AO}^2 = 144 + 25$
⇒ $\text{AO}^2 = 169$
⇒ $\text{AO} = 13\ \mathrm{cm}$
Hence, the correct answer is 13 cm.
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