Find The Angle

Geometry Level 3

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Image link: http://s30.postimg.org/o741xd2k1/Untitled.png

In acute \(\triangle ABC,\) \(\angle BAC = 80^{\circ}.\) The internal angle bisectors of \(\angle ABC\) and \(\angle BCA\) intersect sides \(CA\) and \(AB\) at points \(P,Q\) respectively. Let \(I\) be the incenter of \(\triangle ABC\) (the point where \(BP\) and \(CQ\) meet). Suppose the circumcenter of \(\triangle PQI\) lies on the line joining \(A\) and \(I.\) Find \(\angle ABI\) in degrees.

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