Distances in a right triangle

ABC is a right triangle with ∠*A**B**C*=90∘ with *A**B*=30 sqrt 3and *B**C*=30. *D* is a point on segment *B**C* such that *A**D* is the median. *E* is a point on segment *A**C* such that *B**E* is perpendicular to *A**C*. *A**D* and *B**E* intersect at *F*. If *E**F*=(a sqrt b)/*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*?

Re: Distances in a right triangle

The triangle ABC is 30,90,60 triangle....with BE as height and AD as median...angle BAD is easy to calculate so does the angle FAE.. AC = 60 ,AE = 45 and EC = 15 .

You have whatever you need to find EF.....then compare it with what you have....just elementary algebra..

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Re: Distances in a right triangle

Hi,

Everything in the previous posting is certainly true, but I don't see how this immediately gives the distance EF. Here is a purely algebraic solution:

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