MathNet 2018-part-01 — 181 problems (EN–VI) Question 22

Let $ABC$ be an acute-angled triangle with $\angle BAC = 60^\circ$, incenter $I$ and circumcenter $O$. Let $O'$ be the point diametrically opposed to $O$ on the circumcircle of the triangle $BOC$. Prove that
$$
IO' = BI + IC.
$$