# Finding the measure of $\angle AEB$ given a figure

In the given figure, $O$ is the center of the circle and $$\angle AOB =120$$

How could I find the measure of $\angle AEB$?

With $A,B,O$ fixed, $C$ and $D$ determine $E$, so $\angle AEB$ depends on $C$ and $D$, no? Then what are those? – anon Apr 22 '12 at 3:34
It seems we are missing a piece of information, such as the $\angle$ for $C$ or $D.$ Also, what have you tried so far? – Joe Apr 22 '12 at 3:44
To be more specific about the ambiguity: if $AC$ and $BD$ were diameters (containing $O$), then $\angle AEB = \angle AOB = 120^{\circ}$. On the other hand, if $C$ and $D$ were to coincide (along the longer arc $AB$), then $E$ would coincide with them, so that $\angle AEB = \angle ACB = \angle ADB = 60^{\circ}$ (by the Inscribed Angle Theorem en.wikipedia.org/wiki/Inscribed_angle ). With $C$ and $D$ elsewhere, $\angle AEB$ is something else. This, even though the $\angle C$ and $\angle D$ --with $C$ and $D$ along the longer arc $AB$-- are always $60^{\circ}$ (by the IAT). – Blue Apr 22 '12 at 6:35
As discussed in the comments, the measure of the angle depends on the positions of $C$ and $D$: