Mathematical Olympiad Day I 12:30 PM – 5 PM EDT April 30, 2013 Note: For any geometry problem, the first page of the solution must be a large, in-scale, clearly labeled diagram made with drawing instruments (ruler, compass, protractor, graph paper). Failure to meet any of these requirements will result in a 1-point automatic deduction. USAMO 1. In triangle ABC, points P, Q, R lie on sides BC, CA, AB, respectively. Let ωA , ωB , ωC denote the circumcircles of triangles AQR, BRP, CP Q, respectively.…
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