Wednesday, November 17, 2010
8th Australian Mathematical Olympiad Problems 1987
A1. ABC is an isosceles triangle with AB = AC. M is the midpoint of AC. D is a point on the arc BC of the circumcircle of BMC not containing M, and the ray BD meets the ray AC at E so that DE = MC. Show that MD2 = AC·CE and CE2 = BC·MD/2. A2. Show that (2p)!/(p! p!) - 2 is a multiple of p if p is prime. A3. A graph has 20 points and there is an edge between
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