The line touches the circle at the point K. Point O is the center of the circle. The KM chord forms a tangent angle of 62 °. Find the magnitude of the angle OMK
OK is perpendicular to the tangent (by the tangent property), i.e. the angle between OK and the tangent is 90 °.
Therefore, ∠OKM = 90 ° -62 ° = 28 °
The triangle OMK is isosceles (because OM and OK are the radii of the circle and, respectively, are equal to each other).
By the property of an isosceles triangle ∠OKM = ∠OMK = 28 °
Answer: ∠OMK = 28
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