MathDB
Bosnia and Herzegovina EGMO TST 2018 Problem 3

Source: Bosnia and Herzegovina EGMO Team Selection Test 2018

September 19, 2018
geometrycircumcircleperpendicular bisector

Problem Statement

Let OO be a circumcenter of acute triangle ABCABC and let O1O_1 and O2O_2 be circumcenters of triangles OABOAB and OACOAC, respectively. Circumcircles of triangles OABOAB and OACOAC intersect side BCBC in points DD (D≠BD \neq B) and EE (E≠CE \neq C), respectively. Perpendicular bisector of side BCBC intersects side ACAC in point FF(F≠AF \neq A). Prove that circumcenter of triangle ADEADE lies on ACAC iff FF lies on line O1O2O_1O_2
Back to ProblemsView on AoPS