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Incenter diamter

Source: China Southeast Math Olympiad 2015 Day 1 P2

June 6, 2017
geometryincenter

Problem Statement

Let II be the incenter of △ABC\triangle ABC with AB>ACAB>AC. Let Γ\Gamma be the circle with diameter AIAI. The circumcircle of △ABC\triangle ABC intersects Γ\Gamma at points A,DA,D, with point DD lying on \overarc{AC} (not containing BB). Let the line passing through AA and parallel to BCBC intersect Γ\Gamma at points A,EA,E. If DIDI is the angle bisector of ∠CDE\angle CDE, and ∠ABC=33∘\angle ABC = 33^{\circ}, find the value of ∠BAC\angle BAC.
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