ABC is a right triangle with ∠ABC=90∘ with AB=18sqrt3 and BC=18. D is a point on segment BC such that AD is the median. E is a point on segment AC such that BE is perpendicular to AC. AD and BE intersect at F. If EF=asqrtb/c, where a and c are positive, coprime integers and b is not divisible by the square of any prime, what is the value of a+b+c?
(This question has been asked in a challenge where I have lost all the three attempts to answer this ... So tell please)

Question

ABC is a right triangle with ∠ABC=90∘ with AB=18sqrt3 and BC=18. D is a point on segment BC such that AD is the median. E is a point on segment AC such that BE is perpendicular to AC. AD and BE intersect at F. If EF=asqrtb/c, where a and c are positive, coprime integers and b is not divisible by the square of any prime, what is the value of a+b+c?  
(This question has been asked in a challenge where I have lost all the three attempts to answer this ... So tell please)