Equal Chords

Let ABC be a triangle with incenter I. Let AB and AC intersect the circle through B, I, and C at D and E, respectively, besides B and C. Then BD = CE.

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DETAILS

See problem 2.91(b) in V. Prasolov, Problems in Plane and Solid Geometry, Vol. 1, Plane Geometry [PDF], (D. Leites, ed. and trans.).
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