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Found problems: 1

Durer Math Competition CD 1st Round - geometry, 2014.D3
Tags: octagon , regular octagon , geometry
$ABCDEF GH$ is a regular octagon with $10$ units side . The circle with center $A$ and radius $AC$ intersects the circle with center $D$ and radius $CD$ at point $ I$, different from $C$. What is the length of the segment $IF$?