MK is the chord of the circle with the center O. Find the angle OMK if the angle MOK = 40 degrees.
| May 10, 2021 | education
Construct the radii of the circle OK and OM to the ends of the chord MK. Then OM = OK = R, and therefore the MOK triangle is isosceles with the base MK. Then the angle ОМК = ОМК.
The sum of the interior angles of the triangle is 180, then OMK + OKM + MOK = 180.
2 * OMK = 180 – MOK = 180 – 40 = 140.
OMC angle = 140/2 = 70.
Answer: The angle ОМK is 70.
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