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G3

Part of 2012 IMO Shortlist

Problems(1)

IMO Shortlist 2012, Geometry 3

Source: IMO Shortlist 2012, Geometry 3

7/29/2013
In an acute triangle ABCABC the points D,ED,E and FF are the feet of the altitudes through A,BA,B and CC respectively. The incenters of the triangles AEFAEF and BDFBDF are I1I_1 and I2I_2 respectively; the circumcenters of the triangles ACI1ACI_1 and BCI2BCI_2 are O1O_1 and O2O_2 respectively. Prove that I1I2I_1I_2 and O1O2O_1O_2 are parallel.
geometrycircumcirclehomothetyIMO Shortlistradical axisSpiral Similarity