MK-chord of a circle centered on O. Find the angle OMC if the angle MC = 40 degrees.

Draw the radii OM and OK to the ends of the chord MK.

Then, in the OMC triangle, the side OM = OK, and therefore, the OMC triangle is isosceles with the base of the MC.

In an isosceles triangle of coal at the base are equal, the angle ОМК = ОМК.

The sum of the interior angles of the triangle is 180, then the angle MOK + OMK + OKM = 180.

2 * OMK = 180 – MOK = 180 – 40 = 140.

OMC angle = 140/2 = 70.

Answer: The angle MOC is 70.

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