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Let A(z1) be the point of intersection ...

Let `A(z_1)` be the point of intersection of curves `arg(z-2 + i) = (3pi)/4 ) and arg (z+isqrt3)=pi/3, B(z_2)` be the point on the curve `arg (z+isqrt3)=pi/3`such that `|z_2-5|=3` is minimum and `C(z_2)` be the centre of circle `|z-5|=3`. The area of triangle ABC is equal to

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