AB and BC are tangent line segments drawn to a circle of radius 8 cm.Find AB and BC if BO is 16 cm.

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.

By the Pythagorean theorem, we determine the length of the leg AB. AB ^ 2 = OB ^ 2 – OA ^ 2 = 256 – 64 = 192.

AB = 8 * √3 cm.

BC = AB = 8 * √3 cm.

Answer: The length of the segments AB and BC is 8 * √3 cm.

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