Antipodal Points

You are given a set of $N$ distinct points $P_1, P_2, P_3, \ldots, P_N$ on a $2$-D plane. A triplet $(i, j, k)$ is called a holy triplet if - $1 \leq i \lt j \lt k \leq N$ - $P_i$, $P_j$ and $P_k$ are non-collinear and - Any two of the points $P_i$, $P_j$ and $P_k$ are [antipodal](https://en.wikipedia.org/wiki/Antipodal_point) points of the circle that passes through all three of them. Two point