Let $ ABCD$ be a quadrilateral inscribed in a circle. The diagonal $ BD$ bisects $ AC$. If $ AB = 10$, $ AD = 12$ and $ DC = 11$, find $ BC$.
Source: 2009 Puerto Rico Team Selection Test p5
Tags: geometry, cyclic quadrilateral
Let $ ABCD$ be a quadrilateral inscribed in a circle. The diagonal $ BD$ bisects $ AC$. If $ AB = 10$, $ AD = 12$ and $ DC = 11$, find $ BC$.