A cyclic quadrilateral and two diagonals. What fraction of its area is blue?

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## Solution

The blue fraction is a^{2}/b^{2}.

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 a^{2}/b^{2}. The same goes for triangles DBF and EBD. Adding the two results gives the required answer.

## Poem

Similar intentions of morality and ethics

Helpful for common organizations

With some intentions

And Europe discusses with each delegations

Trying not to repeat the same errors

No more war

Terrible pictures

Cities burned

People wounded and killed

Our intentions are peace