MathNet 2015-part-03 — 191 problems (EN–VI) Question 57

Let $k$ be a real number such that $-1 \lt k \lt 1$. The straight line $y = x + k$ meets the curve $y = 1 - x^2$ at $A$ and $B$. If $C$ denotes the point $(1, 0)$, find the greatest possible area of $\triangle ABC$.