Hi guys! Yesterday I found a cool problem:

in the square ABCD, Q and P cut AD and DC in half. Calculate the ratio of areas BEFG/ABCD.

Now, despite this is correct, I find it a little complicated, and I think that some calculations could be avoided. For example, could you show that GF=FE without explicitly calculating it as I did? Or, how would you show that BF lies on BD?

In general, how would you solve the whole problem?

edit: maybe a mod could put a spoiler on my solution... i don't know how to do that

Hope you like this :-)