Question : A chord of the larger among two concentric circles is of length 10 cm and it is tangent to the smaller circle. What is the area (in cm2) of the annular portion between the two circles?
Option 1: $10 \pi$
Option 2: $25 \pi$
Option 3: $5 \pi$
Option 4: $\frac{5 \pi}{2}$
Correct Answer: $25 \pi$
Solution :
Let the radius of the bigger circle be 'R' and the smaller circle be 'r'.
Let AB be a chord of the bigger circle that is tangent to the smaller circle.
⇒ AB = 10 cm
⇒ AM = $\frac{10}{2}$ = 5 cm
In triangle OAM
⇒ OA
2
= OM
2
+ AM
2
⇒ R
2
= r
2
+ 5
2
⇒ R
2
– r
2
= 25
Area between the two circle = $\pi(R^2 - r^2) = 25 \pi$ cm
2
Hence, the correct answer is $ 25 \pi$.
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