Circle Problems

Can you solve them and describe ways in which each might be connected to one or both of the others?

 

                     

Explain why ab = cd?

                 
            (where a,b,c,d are lengths)

2) These three circles are drawn so that they touch each other and their centres are all on the line AB.
If CD is 8 units in length, what is the area of the part that is shaded yellow?

If the area shaded yellow is equal to the area of the larger of the two circles that are shaded blue, what is the relationship between the radii of the three circles?

 

The solution from the Romanian team is here: