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Find angle in isosceles triangle ABC

Source: (Indian) RMO 2009 Problem 1

November 29, 2009
trigonometrygeometryangle bisectorperpendicular bisectorgeometry unsolved

Problem Statement

Let ABC ABC be a triangle in which AB \equal{} AC and let I I be its in-centre. Suppose BC \equal{} AB \plus{} AI. Find ∠BAC \angle{BAC}
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