AB and BC are tangent line segments drawn to a circle of radius 8 cm.Find AB and BC if BO is 16 cm.
May 31, 2021 | education
| 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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