linear algebra - Trouble in this circle question

Referring to this diagram (self-made):

Question says:

In the given figure diameter of the circle is $3$ cm. AB & MN are two diameter such that MN is perpendicular to AB. In addition CG is parallel to MN. $AE : EB = 1 : 2$ and DF is perpendicular to MN and $NL : ML = 1 : 2$, find the length of DH.

Using the ratios, I could formulate that $AE = 1 cm$ and $EB = 2cm$ and $NL = 1cm$ and $ML = 2cm$.
I could also find that $MO = A0 = BO = ON = 1.5cm$
Also, EOLH becomes a square of side 0.5 cm.

But can't figure out how to find DH.

Can someone please help.

Thanks a lot.

Answer

$OD$ is a radius of the circle as well, so has length $1.5$. $OL$ has length $0.5$. So by Pythagoras $DL$ has length $\sqrt{1.5^2 - 0.5^2} = \sqrt{2}$. And $HL$ has length $0.5$ so $DH$ has length $\sqrt 2 - 0.5$.