# AB and BC are segments of tangents drawn from point B to a circle with center O.

AB and BC are segments of tangents drawn from point B to a circle with center O. OA = 16cm, and radii drawn to points of tangency form an angle equal to 120 degrees. What is the OB segment?

The radii OA and OC are perpendicular to the tangent AB and BC, then the triangles AOB and COB are rectangular, in which the hypotenuse of OB is common, OA = OC = R, then the triangles AOB and COB are equal in leg and hypotenuse.

Then the angle AOB = COB = 120/2 = 60, angle ABO = (90 – 60) = 30.

OA leg lies opposite angle 30, then its length is equal to half the length of the OB hypotenuse.

ОВ = 2 * ОА = 2 * 16 = 32 cm.

Answer: The length of the OB segment is 32 cm.

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