A point O lies inside of the square ABCD. Prove that the difference between the sum of angles OAB,OBC,OCD,ODA and 180∘ does not exceed 45∘.
Source: ToT 2003-JA-5
Tags: inequalities, geometry unsolved, geometry
A point O lies inside of the square ABCD. Prove that the difference between the sum of angles OAB,OBC,OCD,ODA and 180∘ does not exceed 45∘.