Proof Revision!

Geometry Level 3

Take a look at the following proof.

We're going to try to prove that if OO is a point inside ABD\triangle ABD, then AD+AB>OD+OBAD+AB>OD+OB.

First join OO and AA.

From the triangle inequality,

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

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

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


Switch sides to get,



Here are some comments about the proof.

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

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

[3][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.


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