it 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 arc to the circumference of the circle A but off by the circle

Options

A. `1/2`
B. `1/4`
C. `1/3`
D. `2/3`

Answer

C

Explanation

When two circles A and B of equal radii pass through the centres of each other, the angle made by arc of B at the centre of B is `90^(@)`.
So, length of small arc of `B = (2pir90^(@))/(360^(@))= (pir)/(2)`
Hence, circumference of A cut off by the circle B
`= 2pir - (pir)/(2) = (3pir)/(2)`
`:.` Required ratio `= (pir//2)/(3pir//2) = 1/3`