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I have posted a link there to this thread so the OP can view my work.How to solve this maths problem?

So we have a triangle ABC with given sides. On the BC side, there's a part of a circle (we do not know how much of a circle). We are asked to find the angle A to ensure that the part of a circle has the same area as the triangle. The problem boils down to finding how to calculate the area of the part of circle. So how would you go about doing it?

Thanks