Two chords, PQ and RS, meet at a point T outside the circle. Given |TO|=6, |PQ|=8, |TR|=6, find |RS|.

I mean does question make sense? Is the problem well worded?
The only problem I see with the wording is that they don't tell you what O is. I suppose it is the center of the circle.

Well, another issue is that chords are segments that lie entirely inside the circle, so if they intersect outside the circle, they must mean they meet when extended. That may be considered acceptable.

It also doesn't tell you which of R and S is closer to T, but that can be deduced.

It isn't a particularly easy problem, from what I see yet. But that isn't what you asked.
 
So is the problem solvable?
I think something else must be wrong besides the things I tried to correct, because |PQ| seems irrelevant, and as a result, there is too little information. Possibly O is a typo for some other point.

You should probably stop using this book. It isn't going to help you learn anything if half the problems are wrong.
 
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