MathDB
MN passes through a constant point- Iran NMO 2005 - Problem2

Source:

September 21, 2010
geometrycircumcirclegeometry proposed

Problem Statement

In triangle ABCABC, ∠A=60∘\angle A=60^{\circ}. The point DD changes on the segment BCBC. Let O1,O2O_1,O_2 be the circumcenters of the triangles ΔABD,ΔACD\Delta ABD,\Delta ACD, respectively. Let MM be the meet point of BO1,CO2BO_1,CO_2 and let NN be the circumcenter of ΔDO1O2\Delta DO_1O_2. Prove that, by changing DD on BCBC, the line MNMN passes through a constant point.
Back to ProblemsView on AoPS