# #2 (2016 Iran MO 3rd-G1)

### 感想

これは、どのような点を通るか考えるのが少し難しいところ.
しかし気づけば簡単.

### 原文

In triangle $ABC$ , $w$ is a circle which passes through $B,C$ and intersects $AB,AC$ at $E,F$ respectively. $BF,CE$ intersect the circumcircle of $ABC$ at $B',C'$ respectively. Let $A'$ be a point on $BC$ such that $\angle C'A'B=\angle B'A'C$.
Prove that if we change $w$, then all the circumcircles of triangles $A'B'C'$ passes through a common point.

### 和訳

このとき, $w$ の位置にかかわらず, すべての三角形 $A'B'C'$ の外接円はある一点を通ることを示せ.