A tangent CD is drawn to a circle with center O (D-tangency point). Find the line segment OC if the radius of the circle is 6 cm and the angle DCO = 30.
Construct the radius of OD to the point of tangency D.
The radius of the circle drawn to the tangency point is perpendicular to the tangent itself, then the COD triangle is rectangular.
In a right-angled triangle COD, the leg OD lies against the angle 30, then its length is equal to half the length of the hypotenuse OC.
OD = OC / 2.
OC = 2 * OD = 2 * 6 = 12 cm.
Answer: The length of the OC segment is 12 cm.
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