# AB-tangent to the circle with center O, B – tangency point, OA = 17 cm. Find the length AB

AB-tangent to the circle with center O, B – tangency point, OA = 17 cm. Find the length AB, if a) the radius of the circle is 15 cm; c) angle AOB = 30 degrees.

a) Triangle AOB is rectangular, since AB is tangent to the circle, and OB is the radius of the circle drawn to the point of tangency B.

Then, by the Pythagorean theorem, AB ^ 2 = OA ^ 2 – OB ^ 2 = 17 ^ 2 – 15 ^ 2 = 289 – 225 = 64.

AB = 8 cm.

In a right-angled triangle AOB, the angle OB = 300, and the leg AB lies against this angle, then the leg length is equal to half the length of the OA.

AB = OA / 2 = 17/2 = 8.5 cm.

Answer: a) AB is 8 cm, c) AB is 8.5 cm.

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