Sharygin 2006, correspondence round, problem 7
Sharygin 2006, correspondence round, problem 7 is a plane geometry problem from the Sharygin Geometry Olympiad 2006, correspondence round, problem 7 (grades 8–10): congruent triangles ABE and BCF on a square.
Problem
Given are a point $E$ inside the square $ABCD$ and a point $F$ outside it, so that triangles $ABE$ and $BCF$ are equal. Find the angles of the triangle $ABE$ if it is known that the segment $EF$ is equal to the side of the square, while the angle $BFD$ is right.
Source Sharygin Geometry Olympiad 2006, correspondence round, problem 7 (grades 8–10)
The diagram
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