Hello,

Please have a look at the sketch.

BE is the altitude of the triangle coming from B.

Thus

Note that you want . Obviously, it is equal to because the triangle BED is a right angle triangle in E.

Now, you'll have to calculate ED, since you already know the others.

D is the midpoint of AC. Therefore

And

If we multiply by 2, we can write

Applying Pythagoras theorem in AEB, we have

Applying Pythagoras theorem in BEC, we have

--------------------------------------------------------------

See the two boxed formula ?

This gives :

Multiply by

And please observe

(in fact, the important step was to multiply the denominator by its conjugate, and it just popped up that it was the length b)

---------------------------------------------------------------------------

There may be a shorter way, but I don't know... Inspire yourself from it