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Circumcircle of ILK is tangent to ABC iff AB+AC=3BC

Source: Iranian National Olympiad (3rd Round) 2004

January 9, 2009
geometrycircumcircleinradiusincenterratiotrigonometryIMO Shortlist

Problem Statement

Incircle of triangle ABC ABC touches AB,AC AB,AC at P,Q P,Q. BI,CI BI, CI intersect with PQ PQ at K,L K,L. Prove that circumcircle of ILK ILK is tangent to incircle of ABC ABC if and only if AB\plus{}AC\equal{}3BC.
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