Question 141
Find all triangles $ABC$ such that the angle $\angle BCA$ is acute, the perpendicular bisector of the segment $BC$ cuts the two rays dividing the angle $\angle BAC$ into three equal angles ($\angle BAx = \angle xAy = \angle yAC$) at the points $N$ and $P$ satisfying the conditions $AB = NP = 2HM$, where $H$ is the orthogonal projection of $A$ on $BC$ and $M$ is the midpoint of $BC$.