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.

It's unclear how A is defined, and given your diagram ABCD is not a cyclic quadrilateral. — Alvin Chen, Jan 02 '20 at 15:22

score 1 · Accepted Answer · answered Jan 02 '20 at 15:49

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: $HB = 49/\sqrt{74}$

answered Jan 02 '20 at 15:49

Matteo

6,581

could you please check the configuration (I edited the post) – ahmed Jan 02 '20 at 19:08
1

The conclusion is the same – Matteo Jan 03 '20 at 20:11

find distance given distances and right angles

1 Answers1