Hello everyone, I happened to come across this problem from the 5lb book:

**I marked D** because I thought as far as quantity A is concerned, if BE increases, then AD increases and we’d never know how long BC or AC (both could be long or short) is. So, I explicated that A and B could be different in different scenarios.

**But the answer is C**. I’d be grateful towards any of your valuable explanations. Thanks!

Hint: look at similar triangles (which may not be obvious at first glance).

Heyy thanks, I got the answer. I sketched this out though

Pardon me for the messy sketch, but thanks for the hint. I have another question though, @Leaderboard how do I recognize / when do I assume that they can be similar?

By doing what you did above.

Yep, yes. But I mean, I used your hint to do those calculations, though. How do I know where to consider similar triangles?

In most cases, the context would be obvious. This is one of those cases where it’s tricky if you haven’t practiced - so that’s what I would recommend instead.