# A tangent MK is drawn through the point M of the circle with the center O. Find the radius of the circle

December 29, 2020 | education

| **A tangent MK is drawn through the point M of the circle with the center O. Find the radius of the circle, if OK = 14cm, angle MOK = 60 degrees.**

Since the radius drawn to the tangent point of the tangent forms a right angle with it, the KOM triangle is rectangular, in which the IOC angle is 600, and the hypotenuse OK = 14 cm.

The MCO angle of a right-angled triangle MOC will be: MKO = 180 – 90 – 60 = 30.

The leg is OK is equal to the radius of the circle.

The leg of a right-angled triangle, opposite the angle of 300, is equal to half the length of the hypotenuse.

R = ОМ = OK / 2 = 14/2 = 7 cm.

Answer: The radius of the circle is 7 cm.

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