Question

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 :

Answer 1

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)`
As these circles are concentric,
`:. AB = 2AC = 2sqrt(a^2-b^2)`