Online Geometry Problem 933: Square, Center, Transversal, Perpendicular,
Metric Relations, Congruence. Level: High School,
SAT Prep, College,
Mathematics Education

In a square ABCD of center O, BG and
CH are perpendicular to FO extended. CM and CN are perpendicular
to EO extended. If AD = 4, find BG^{2} + CH^{2} + CM^{2} + DN^{2}.