Proof Revision!

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,

\[AD+OA> OD\cdots (1)\]

\[OB+OA>AB\cdots (2)\]

Subtract \((2)\) from \((1)\) to get,

\[AD-OB>OD-AB\]

Switch sides to get,

\[AD+AB>OD+OB\]

\[\mathbb{QED}\]

Here are some comments about the proof.

\([1]\). The proof is not correct. There's an invalid move hiding in there somewhere.

\([2]\). Relax! Not everything in this set is a trick question. This proof is perfectly fine.

\([3]\). 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.