Let ABC be a triangle and P be a point inside it such that AP, BP and CP meet sides BC, CA and AB in points D, E and F, respectively. Given that AP=a, BP=b, CP=c, PD=PE=PF=3 and a+b+c=43, find abc.

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Let ABC be a triangle and P be a point inside it such that AP, BP and CP meet sides BC, CA and AB in points D, E and F, respectively. Given that AP=a, BP=b, CP=c, PD=PE=PF=3 and a+b+c=43, find a*b*c.