# 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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