MathNet 2019-part-08 — 179 problems (EN–VI) Question 55

In triangle $ABC$ with $AB \lt AC$, let $H$ be the orthocenter and $O$ be the circumcenter. Given that the midpoint of $OH$ lies on $BC$, $BC = 1$, and the perimeter of $ABC$ is $6$, find the area of $ABC$.