Problem 1138, Gogeometry, https://gogeometry.blogspot.com/2015/07/geometry-problem-1138-square.html

 Let E, F be points onto extensions of the sides (AB, (AD of the square ABCD so that BE=DF and call G projection of A onto BF. Prove that GE_|_CG.

Proof, new
Construct the square AEKF; let AG cut KE at L. Well known, LE=AB=AD, BELC is a rectangle, BELG cyclic, thus BECG is cyclic, hence <CGE=<CBE, done.