# Be Cautious!

Geometry Level 5

I accidentally created this problem while solving INMO 1999 question 1.

Let $\triangle ABC$ be an acute angled triangle in which $D,\ E,\ F$ are points on $BC,\ CA,\ AB$ respectively such that $AD \perp BC$; $AE=EC$; and $CF$ bisects $\angle C$ internally. Suppose $CF$ meets $AD$ and $BE$ (change) in $M$ and $N$ respectively. If $FM= 2,\ MN= 1,\ NC= 3$, find the perimeter $p$ of the $\triangle ABC$.

Answer $p$ in 3 significant digits. (Round to even method)

Hint: Please do not make any unnecessary assumptions.

Note: For those requesting clarification, I can guarantee that the problem is correct. If you can't solve, see solution.

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