Circle with center C and line AB touch at point B. Find AB if AC = 17 and the diameter of the circle is -16

Let’s construct the diameter BD to the point of tangency of the straight line AB and the circle.

The radius of the circle drawn to the tangent point is perpendicular to the tangent itself.

Then the triangle ABC is rectangular, in which the leg BC = R = D / 2 = 16/2 = 8 cm, AC = 17 cm.

Then, by the Pythagorean theorem, we determine the length of the leg AB.

AB ^ 2 = AC ^ 2 – BC ^ 2 = 289 – 64 = 225.

AB = 15 cm.

Answer: The length of tangent AB is 15 cm.