Question : If the length of a chord drawn at a distance of 21 cm from the centre of a circle is 40 cm, the radius (in cm) of the circle is:
Option 1: 29
Option 2: 21
Option 3: 25
Option 4: 20
Correct Answer: 29
Solution :
Given: AB = 40 cm and OC = 21 cm
Now AC = BC = $\frac{40}{2}$ = 20 cm (perpendicular drawn from the centre of the circle to the chord bisects the chord)
Then using Pythagoras's theorem, we get,
$OA = \sqrt{AC^{2} + OC^{2}} = \sqrt{20^{2} + 21^{2}} = \sqrt{841} = 29$ cm
Hence, the correct answer is 29.
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