Question 114
Let $n$ and $k$ be positive integers. Let $A$ be a set of $2n$ distinct points in the plane, no three of which are collinear. Some pairs of points of $A$ are joined, so that there are $n^2 + k$ distinct segments in the plane. Prove that there are at least $\frac{4}{3}k^{3/2}$ distinct triangles in the plane whose vertices all belong to $A$ and whose three sides are all among the drawn segments.