Consider an obtuse angled triangle $A B C$ in which the difference between the largest and the smallest angle is $\frac{\pi}{2}$ and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1. Let $a$ be the area of the triangle $A B C$. Then what is the value of $(64 a)^{2}$?
JEE · Math · previous-year question
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