The radius ОM, ON, OK is drawn in the circle, find the angle MON if the angle ONM = the angle ONK

The radius ОM, ON, OK is drawn in the circle, find the angle MON if the angle ONM = the angle ONK, the angle KON = 62 degrees.

In the triangle OKH, the sides OH and OK are the radii of the circle, therefore, the triangle OKH is isosceles, then the angle OHK = OKH.

Similarly, in the triangle ОМН, the angle ОНМ = ОМH. By condition, the angle ОМН = ОHК, then in the triangles ОНМ and ОНК the angles at the bases HМ and HК are equal. Since the sum of the inner angles of the triangle is 180, and the angle (ОМH + ОHМ) = (ОHHК + ОКH), then the angle MOH = KOH = 62.

Answer: The MOH angle is 62.