three circles with centers A, B and C have respective radii 50, 30 and 20 inches and are tangent to each other externally. Find the area in (in^2) of the curvilinear triangle formed by the three circles

Question

phi · Answer

I can see how to do it tediously
you know all three sides of a triangle formed by connecting the centers.
use heron's formula to find the area of the triangle.
you can find all three angles (use Law of cosines and Law of sines)
once you know the angles, you can find the area of each sector
the area you want is 
area of triangle - sum of sectors

irishboy123 · Answer

replicated here http://openstudy.com/study#/updates/55d9d670e4b05a670c276399

phi · Answer

fyi, here is what the strategy comes up with