Question : A 9 cm long perpendicular is drawn from the centre of the circle to a 24 cm long chord. Find the radius of the circle.
Option 1: 17 cm
Option 2: 18 cm
Option 3: 16 cm
Option 4: 15 cm
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Correct Answer: 15 cm
Solution :
The perpendicular drawn from the centre of the circle to the chord bisects the chord.
⇒ AM = MB = $\frac{24}{2}$ = 12 cm
In the right triangle AMO,
AO
2
= OM
2
+ AM
2
⇒ AO
2
= 9
2
+ 12
2
⇒ AO
2
= 225
$\therefore$ AO = 15 cm
Hence, the correct answer is 15 cm.
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