MathDB
IMO Shortlist 2009 - Problem G8

Source:

July 5, 2010
geometryincentercircumcircletrigonometryinradiusIMO Shortlist

Problem Statement

Let ABCDABCD be a circumscribed quadrilateral. Let gg be a line through AA which meets the segment BCBC in MM and the line CDCD in NN. Denote by I1I_1, I2I_2 and I3I_3 the incenters of △ABM\triangle ABM, △MNC\triangle MNC and △NDA\triangle NDA, respectively. Prove that the orthocenter of △I1I2I3\triangle I_1I_2I_3 lies on gg.
Proposed by Nikolay Beluhov, Bulgaria
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