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IMO Shortlist 2011, G1

Source: IMO Shortlist 2011, G1

July 13, 2012
geometrycircumcircletrigonometrygeometric transformationIMO Shortlist

Problem Statement

Let ABCABC be an acute triangle. Let ω\omega be a circle whose centre LL lies on the side BCBC. Suppose that ω\omega is tangent to ABAB at B′B' and ACAC at C′C'. Suppose also that the circumcentre OO of triangle ABCABC lies on the shorter arc B′C′B'C' of ω\omega. Prove that the circumcircle of ABCABC and ω\omega meet at two points.
Proposed by Härmel Nestra, Estonia
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