A tangent line AB is drawn from point A to the circle centered at point O, and the segment AO of points B

A tangent line AB is drawn from point A to the circle centered at point O, and the segment AO of points B and K belong to the circle. If AB = 12, OK = 5, then the length of the segment AK is equal.

From the center of the circle, point O, we construct the radius OB to the point of tangency B.

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

Then triangle AOB is rectangular.

ОВ = OK = R = 5 cm.

Let the length of the segment AK = X cm, then the length of the hypotenuse OA = (OK + AK) = (5 + X) cm.

By the Pythagorean theorem, OA ^ 2 = AB ^ 2 + OB ^ 2.

(X + 5) ^ 2 = 144 + 25 = 169 = 132.

X +5 = 13.

X = AK = 13 – 5 = 8 cm.

Answer: The length of the AK segment is 8 cm.