The Power of Proof in Geometry Problem 394: Square with a 90 Degree Arc and Diagonal. Online, School, College

In the given figure, square ABCD is shown. Arc BD, with center at A, and diagonal AC intersect at point F. The extension of DF meets line BC at point G. Prove that BG = 2EF

A square's sharp lines,
Arcs and diagonals align,
Geometry shines.