A cyclic quadrilateral and two diagonals. What fraction of its area is blue?
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The blue fraction is a2/b2.
First note that the blue triangle CDB is isosceles, giving equal angles at C and D. From the cyclicity of the quadrilateral, we get that the angle at E is bisected by the red diagonal.
Now note that from equal angles, triangle CBF is similar to triangle EBC and the area scale factor is a2/b2. The same goes for triangles DBF and EBD. Adding the two results gives the required answer.
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