How Can the Similarity Theorem Prove Segment Proportions in Triangle ABC?

[Misr]

Hi ,there

ABC is a triangle , D is the midpoint of AB , from D draw a st. line to intersect AC at H and BC at O.
Prove that :

AH : HC = BO: OC
http://img299.imageshack.us/img299/5752/similarity.jpg
We need to solve this problem using the similarity theorem "If a line is drawn parallel to one side of a triangle and intersects the other two sides , then it divides them into segments whose lengths are proportional ".

Thanks in advance

 

[ehild]

Hint: Draw a line through D which is parallel to AC.

ehild

 

[Misr]

Its very easy right now
Thanks