Circles tell the area

Geometry Level 5

Circles \(O_1, O_2 ,O_3, O_4\) intersect at points \(A_1, B_1, A_2, B_2, A_3, B_3, A_4, B_4\), as shown above. Points \(A_1,A_2,A_3,A_4\) lie on a circle pictured above. Also, we are given that the circumradius of triangle \(B_1 B_2 B_3 \) is 5, and that the product of the lengths of the sides \(B_1 B_4, B_3 B_4 , B_1 B_3\) are all 40.

Find the area of triangle \(B_1 B_3 B_4\).

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