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How much is angleA - Iran NMO 2001 (Second Round) - Problem5

Source:

October 4, 2010
geometryincentertrigonometrycircumcircleperpendicular bisectorgeometry proposed

Problem Statement

In triangle ABCABC, AB>ACAB>AC. The bisectors of ∠B,∠C\angle{B},\angle{C} intersect the sides AC,ABAC,AB at P,QP,Q, respectively. Let II be the incenter of ΔABC\Delta ABC. Suppose that IP=IQIP=IQ. How much isthe value of ∠A\angle A?
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