Based on the nine point below, show that the nine-point circle cuts the sides of the triangle at angles (B-C, IC-A and A - B). In other words, show that \angle H O_{1} M_{1}=|B-C|, \angle H O_{2} M_{2}=|C-A| \text {, and } \angle H O_{3} M_{3}=|A-B| (Note: A, B, C referring to angles at vertices A, B, and C, respectively.)