2018 IMO Problems/Problem 1

Revision as of 00:04, 10 July 2018 by Jazzachi (talk | contribs) (Started page)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Let $\Gamma$ be the circumcircle of acute triangle $ABC$. Points $D$ and $E$ are on segments $AB$ and $AC$ respectively such that $AD = AE$. The perpendicular bisectors of $BD$ and $CE$ intersect minor arcs $AB$ and $AC$ of $\Gamma$ at points $F$ and $G$ respectively. Prove that lines $DE$ and $FG$ are either parallel or they are the same line.

Solution