Conic Sections Question 304
Question: If two circles A, B of equal radii pass through the centres of each other, then what is the ratio of the length of the smaller are to the circumference of the circle A cut off by the circle B-
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{4} $
C) $ \frac{1}{3} $
D) $ \frac{2}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
When two circles A and B of equal radii pass through the centers of each other. The angle made by arc of B at the centre of B is $ 90{}^\circ $. So, length of small arc of B= $ \frac{2\pi r \times 90{}^\circ }{360{}^\circ }=\frac{\pi r}{2} $
Hence, circumference of A cut off by the circle B $ =2\pi r-\frac{\pi r}{2}=\frac{3\pi r}{2} $
$ \therefore $ Required ratio $ =\frac{\pi r/2}{3\pi r/2}=\frac{1}{3} $
BETA
