arslan wrote: If d>0 and 0 < 1-c/d < 1, which of the following must be true:
1. c>0
2. c/d < 1
3. c^2+d^2 >1

From the notation you have used, it's hard to tell what the given conditions are.
"1-c/d" could be interpreted as (1-c)/d, or it could be interpreted as 1-(c/d).
Once this is clarified, we can go about answering your question.

Cheers,
Brent

arslan wrote: If d>0 and 0 < 1-(c/d) < 1, which of the following must be true:

1. c>0
2. c/d < 1
3. c^2+d^2 >1

Let's deal with this in parts:

Part 1: 0 < 1-(c/d)
Add c/d to both sides to get: c/d < 1
Since we're told that d is positive, we'll multiply both sides by d to get: c < d

Part 2: 1-(c/d) < 1
Add c/d to both sides to get: 1 < 1 + c/d
Subtract 1 from both sides to get: 0 < c/d
If d is positive and c/d is positive, then c must be positive.
In other words, 0 < c

Combining the two parts, we get 0 < c < d

What kinds of conclusions can we make from this information?

1. c>0 (yes, this must be true)
2. c/d < 1 (since c < d, and since c and d are both positive, this must be true)
3. c^2+d^2 >1 (no, this need not be true. For example, we could have c=0.1 and d=0.2, in which case c^2 + d^2 is not greater than 1.)

Cheers,
Brent