A Triangle and a Trapezoid with a Common Conic

1) Sava Grozdev, 2) Veselin Nenkov

1) University of Finance, Business and Entrepreneurship – Sofia (Bulgaria)
2) „Nikola Vaptsarov“ Naval Academy – Varna (Bulgaria)

Abstract. The aim of the present note is to propose a generalization of Problem 1 on the IMO’2018 paper. The International Mathematical Olympiad (IMO) is the most prestigious scientific Olympiad for high school students. Its 59th edition took place in Cluj-Napoca, Romania, 3–14 July 2018. The problem 1 on the paper was solved fully (7 points) by 381 participants, 7 students were marked with 6 points, 7 with 5 points, 10 with 4 points, 15 with 3 points, 24 with 2 points, 54 with 1 point and 96 with 0 points. The mean result of all the 594 participants in the Olympiad from 107 countries is 4, 934, which shows that the problem is easy and has not bordered most of the contestants. Nevertheless it turns out to be interesting and originates rich in content ideas.

Keywords: Olympiad; problem solving; triangle; trapezoid; conic

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