Question 177
Suppose $P_1, \dots, P_n$ are $n$ points inside triangle $ABC$, such that any three points among $P_1, \dots, P_n, A, B, C$ are not collinear. Prove: It is possible to divide $\triangle ABC$ into a union of $2n+1$ smaller triangles such that each smaller triangle has its vertices among $P_1, \dots, P_n, A, B, C$, and the number of smaller triangles with vertices including at least one point among $A, B, C$ is no less than $n + \sqrt{n} + 1$.