In the figure , two concentric circles of radii a&b(a>b) are given.The chord AB of larger circle touches the smaller circle at C .The length AB is :

Explanation

Let the chord `AB` touches the smaller circle at `C`.

Let `O` is the center of both circles.

The, `OA = a, OC = b`

Also, `AB` is tangent to smaller circle.
`:. /_OCA = 90^@`

`:. OA^2= AC^2+OC^2`

`=> a^2 = AC^2+b^2`

`=>AC = sqrt(a^2-b^2)`

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