Challenge Level

**Here are three problems involving circles.**

Can you solve them?

Can you find relationships between the three problems?

**Firstly** Show that ab = cd (where a, b, c, d are lengths)

Secondly:

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 region shaded yellow?

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