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Incircle-excircle config geo

Source: Serbia 2024 MO Problem 4

April 4, 2024
geometry

Problem Statement

Let ABCABC be a triangle with incenter and AA-excenter I,IaI, I_a, whose incircle touches BC,CA,ABBC, CA, AB at D,E,FD, E, F. The line EFEF meets BCBC at PP and XX is the midpoint of PDPD. Show that XI⊥DIaXI \perp DI_a.
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