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Compute all possible lengths of sides AB and AC

Source: Mediterranean MO 2007

October 31, 2010
geometryinradiustrigonometryquadraticsgeometry unsolved

Problem Statement

In the triangle ABCABC, the angle α=∠BAC\alpha = \angle BAC and the side a=BCa = BC are given. Assume that a=rRa = \sqrt{rR}, where rr is the inradius and RR the circumradius. Compute all possible lengths of sides ABAB and AC.AC.
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