MathDB
Geometry

Source: JBMO 2010 Shortlist

October 18, 2012
geometrycircumcircleparallelogramperpendicular bisectorgeometry unsolved

Problem Statement

Let ABCABC be acute-angled triangle . A circle ω1(O1,R1)\omega_1(O_1,R_1) passes through points BB and CC and meets the sides ABAB and ACAC at points DD and EE ,respectively . Let ω2(O2,R2)\omega_2(O_2,R_2) be the circumcircle of triangle ADEADE . Prove that O1O2O_1O_2 is equal to the circumradius of triangle ABCABC .
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