A) \[\frac{1}{2}\]
B) \[\frac{1}{4}\]
C) \[\frac{1}{3}\]
D) \[\frac{2}{3}\]
Correct Answer: C
Solution :
[c] 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 are of B= \[\frac{2\pi 90{}^\circ }{360{}^\circ }=\frac{\pi r}{2}\] 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 \[=\frac{\pi r/2}{3\pi r/2}=\frac{1}{3}\]
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