Take a look at the following proof.
We're going to try to prove that if \(O\) is a point inside \(\triangle ABD\), then \(AD+AB>OD+OB\).
First join \(O\) and \(A\).
From the triangle inequality,
\[AD+OA> OD\cdots (1)\]
Subtract \((2)\) from \((1)\) to get,
Switch sides to get,
Here are some comments about the proof.
\(\). The proof is not correct. There's an invalid move hiding in there somewhere.
\(\). Relax! Not everything in this set is a trick question. This proof is perfectly fine.
\(\). Forget the proof! The claim itself is not true!
Which comment here is correct?
This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.