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Find the angle

Source: INMO 1991 Problem 5

October 3, 2005
geometryincenter

Problem Statement

Triangle ABCABC has an incenter II. Let points XX, YY be located on the line segments ABAB, ACAC respectively, so that BX⋅AB=IB2BX \cdot AB = IB^2 and CY⋅AC=IC2CY \cdot AC = IC^2. Given that the points X,I,YX, I, Y lie on a straight line, find the possible values of the measure of angle AA.
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