IMO 2011 Shortlist G2
Let A1A2A3A4 be a non-cyclic quadrilateral. Let O1 and r1 be the circumcenter and the circumradius of the triangle A2A3A...
Category: Geometry
Problem
Let A1A2A3A4 be a non-cyclic quadrilateral. Let O1 and r1 be the circumcenter and the circumradius of the triangle A2A3A4. Define O2, O3, O4 and r2, r3, r4 in a similar way. Prove that O1A2 1 − r2 + O2A2 2 − r2 + O3A2 3 − r2 + O4A2 4 − r2 = 0.