The Smallest Circumcircle

Problem

In $\triangle ABC$ with the usual side notation, suppose

2ab\sin A + (ac - 6)\sin 2B = 2b^2 \sin A\cos C,

and $b = 2$ . Find the minimum possible area of the circumcircle of $\triangle ABC$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, trigonometry

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