Dear Alex,

Sorry, still nothing! I do not understand anything! Are you sure there is not a flaw in the argument? I have a feeling there is. Could you please send me a diagram and an explanation? You may draw it by hand and fax it through at +30-210-7219225 if this is easier for you.

The formula is proven very easily by using the cosine rule.

m^2=b^2+c^2-2.b.c.cosC
=a^2+d^2-2.a.d.cosA=a^2+d^2-2.a.d.cos(180-C)=a^2+d^2+2.a.d.cosC
Multiply the first with ad and the second with bc, add them up and you will arrive at m^2=(ab+cd).(ac+bd)/(ad+bc)

I am really surprised. I do not understand what cosè signifies. There might be an error in the proof.

Have a bash at the probability question I posed. I think I have got an answer, it depends on what one is really asking. I look forward to see the replies.