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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