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Intermediate

Similar intention

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

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Solution

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.

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

Bella

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