The past three
International Mathematical Olympiad papers are available for download:
The IMO jury traditionally places the papers in the public domain, and Highperception asserts no copyright over these exams. Highperception materials on these papers will soon be available. The IMO is the annual world championships of secondary school mathematics. The questions are extraordinarily difficult compared with the questions that most school-aged students address. Problems 1 and 4 are relatively easy (but eye watering), problems 2 and 5 are designated medium (i.e. impossible for all but the best) and problems 3 and 6 are designated hard (i.e. impossible for almost everyone). In a normal year, only a handful of competitors solve these problems 3 or 6. Good luck!
This is the eyeball theorem. Irrespective of the sizes of the circles, C1D1 = C2D2. Why?
Drawing by CJB.