Poland II round - 1995-1996
Source: Very good problem
September 8, 2007
trigonometrygeometry proposedgeometry
Problem Statement
A circle with center O inscribed in a convex quadrilateral ABCD is tangent to the lines
AB, BC, CD, DA at points K, L, M, N respectively. Assume that the lines KL and MN
are not parallel and intersect at the point S. Prove that BD is perpendicular OS.
I think it is very good and beautiful problem. I solved it without help. I'm wondering is it a well known theorem? Also I'm interested who is the creator of this problem? I'll be glad to see simple solution of this problem.