Be Cautious!

Geometry Level 5

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

Let ABC\triangle ABC be an acute angled triangle in which D, E, FD,\ E,\ F are points on BC, CA, ABBC,\ CA,\ AB respectively such that ADBCAD \perp BC; AE=EC AE=EC; and CFCF bisects C\angle C internally. Suppose CFCF meets ADAD and BEBE (change) in MM and NN respectively. If FM=2, MN=1, NC=3FM= 2,\ MN= 1,\ NC= 3, find the perimeter pp of the ABC\triangle ABC.

Answer pp 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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