![In the given fig. $XYZ$ is a triangle, $XO$ bisects $\angle YXZ$, $OY$ is perpendicular to $XE$ and $OM\parallel XZ$, to prove : $YM = MZ$. ( I tried but this question seems to be asymptotic or the given conditions are insufficient, please try this!!)](https://i.stack.imgur.com/AfbuQ.jpg)

In the given fig. $XYZ$ is a triangle, $XO$ bisects $\angle YXZ$, $OY$ is perpendicular to $XE$ and $OM\parallel XZ$, to prove : $YM = MZ$. ( I tried but this question seems to be asymptotic or the given conditions are insufficient, please try this!!

A more accurate figure:

![enter image description here](https://i.stack.imgur.com/yhk0d.png)