Let-I-be-the-incenter-of-ABC-It-is-known-that-for-every-point-M-AB-one-can-find-the-points-N-BC-and-P-AC-such-that-I-is-the-centroid-of-MNP-Prove-that-ABC-is-an-equilateral-triangle-

Question Number 16873 by Tinkutara last updated on 27/Jun/17

Let I be the incenter of Δ A B C . It is

known that for every point M \in (A B),

one can find the points N \in (B C) and

P \in (A C) such that I is the centroid of

Δ M N P . Prove that A B C is an

equilateral triangle .