find distance given distances and right angles

Question

In the following figure, it is given three right angles and distances :

$ED = 3 $ , $ EB = 7$ and $CE = 5$.

Is it possible to calculate the length $EA$.

I tried using cyclic quadrilateral $ABCD$ and angles but couldn't find the expression.

thanks for any ideas.

Answer 1

Draw the height relative to the hypotenuse of triangle $CEB$, and let $H$ the foot. The triangle $HEB$ and $AEB$ (I can show that $AEB = EBH$ and $ABE = BEH$) are congruent, so: $HB = EA$. But, for Euclidean's theorems: $HB = 49/\sqrt{74}$