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Equal to distance between the incenter and the circumcenter

Source: Turkey National Olympiad 2002 - D2 - P2

March 6, 2011
geometryincentercircumcircleratiogeometry proposed

Problem Statement

Let ABCABC be a triangle, and points D,ED,E are on BA,CABA,CA respectively such that DB=BC=CEDB=BC=CE. Let O,IO,I be the circumcenter, incenter of △ABC\triangle ABC. Prove that the circumradius of △ADE\triangle ADE is equal to OIOI.
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