A tangent AB is drawn to a circle of radius 5 centered at point O. Find the length of the largest of the segments of the secant

A tangent AB is drawn to a circle of radius 5 centered at point O. Find the length of the largest of the segments of the secant of this circle passing through points A and O, if it is known that AB = 12.

Given:
r = 5
О – center of the circle
AB – tangent
AB = 12.
To find:
The length of the largest of the secant line segments passing through points A and O.

Decision:
The secant is drawn through the center of the circle O.
The tangent line is at an angle of 90 °
Next, we connect O and B, y on a right-angled triangle.
By the Pythagorean theorem:
AB = √169-144 = √25 = 5.

Answer: The length of the largest of the sections of the secant passing through points A and O is 5.