# Proof Revision!

Geometry Level 3

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,

$AD+AB>OD+OB$

$\mathbb{QED}$

$$[1]$$. 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.

×