# How do I find the side of a right triangle?

triangles ABC, ACD and BCD are right triangles, E is the midpoint of segment AB.

If AB = 20cm, find CE.

I'm having a hard time understanding these relationships between the sides of right triangles. Help again

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You posted an analogous question earlier today: math.stackexchange.com/questions/153070/… Did that answer not make sense? – math-visitor Jun 2 '12 at 23:43
It helped yes, but I tried to follow similar format and can't come up with the answer. – Jorge Jun 2 '12 at 23:59
In its current form, $D$ and the triangles $ACD$ and $BCD$ seem redundant, and we do not have enough information to solve the problem. – TMM Jun 3 '12 at 0:21
Is there some sort of convention about where the right angle is when you write triangles with their vertices? Or is this intentionally ambiguous? – rschwieb Jun 3 '12 at 0:40

As a partial answer (since the situation is almost certainly underdetermined as written), if $\angle C$ in $\triangle ABC$ is a right angle, then $\overline{AB}$ is a diameter of the circle that circumscribes $\triangle ABC$, so $E$ is the center of the circle and $CE=\frac{1}{2}AB=\frac{1}{2}\cdot20\text{ cm}=10\text{ cm}$.