In a circle with centre `O ,` AB` and `C D` are two diameters perpendicular to each other. The length of chord `A C` is
(a)`2A B` (b) `sqrt(2)AB` (c) `1/2A B` (d) `1/(sqrt(2))\ A B`

Explanation

In a circle with centre `O, AB \and\ CD` are two diameters perpendicular to each other
`AC^2=OA^2+OC^2=2OA^2`.....(i)
Since,`OC=OA=(AB)/2`
squaring and multiplying `2` on both sides, we get
`2OA^2=2((AB)/2)^2=AB^2/2`
Substitute, `2OA^2=(AB)^2/2`
in equation(i),we get`AC^2=(AB)^2/2`
`AC=1/sqrt2AB`