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Incircle of quadrilateral

Source: North Korea Team Selection Test 2013 #5

May 17, 2014
geometryquadrilateralincircle

Problem Statement

The incircle ω \omega of a quadrilateral ABCD ABCD touches AB,BC,CD,DA AB, BC, CD, DA at E,F,G,H E, F, G, H , respectively. Choose an arbitrary point X X on the segment AC AC inside ω \omega . The segments XB,XD XB, XD meet ω \omega at I,J I, J respectively. Prove that FJ,IG,AC FJ, IG, AC are concurrent.
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