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Sample Question 25:
Circles ω1, ω2, and ω3 each have radius 4 and are placed in the plane so that each circle is externally tangent to the other two. Points P1, P2, and P3 lie on ω1, ω2, and ω3 respectively such that P1P2=P2P3=P3P1 and line PiPi+1 is tangent to ωi for each i=1,2,3, where P4=P1. See the figure below. The area of △P1P2P3 can be written in the form a+b for positive integers a and b. What is a+b?