Two concentric circles are of radii `7cm` and `r cm` respectively, where `r gt 7`. A chord of the larger circle of length `46cm`, touches the smaller circle. Find the value of `r`.

Explanation

Let `O` be the common centre of the two circles and `AB` be the chord of the larger circle which touches the smaller circle at `C`.
Then, `AB=46cm`.
Join `OA` and `OC`. Then, `OA=rcm` and `OC=7cm`
Now, `OCbotAB` and `OC` bisects `AB`.
In right `DeltaACO`, we have
`OA^(2)=OC^(2)+AC^(2)` [by Pythagoras, theorem]
`impliesOA=sqrt(OC^(2)+AC^(2))=sqrt(OC^(2)+((1)/(2)AB)^(2))` [`:'C` is the midpoint of `AB`]
`impliesr cm=sqrt(7^(2)+23^(2))cm=sqrt(578)cm=17sqrt(2)impliesr=17sqrt(2)cm`.