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'Partly Circles' printed from http://nrich.maths.org/

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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?