RU-SPB 2016 Problem 115

Grade 11

Incircle of $\triangle ABC$ touch $AC$ at $D$ . $BD$ intersect incircle at $E$ . Points $F,G$ on incircle are such points, that $FE \parallel BC,GE \parallel AB$ . $I_1,I_2$ are incenters of $DEF,DEG$ . Prove that $I_1I_2 \perp$ bisector of $\angle ABC$

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