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Problem was just posed by ganesh.
I know there is a lot of ways to do this but supposing you did not have any idea how to solve this. Geogebra to the rescue!
8) use one of the free vertices to expand the inner circle. Find the new areas. What do you deduce?
Looks like the ratio of the areas is 1 / 2. Not rigorous but definitely enough to go to war with!