A tangent line AB and a secant line AO are drawn to a circle centered at point O. Find the radius

A tangent line AB and a secant line AO are drawn to a circle centered at point O. Find the radius of the circle if AB = 18, AO = 82.

The solution of the problem:

1. Connect points B and O. BО is the radius of the circle r. Tangent AB is perpendicular to the AO radius. Angle B is 90.

2. Consider the triangle AOB.

ОВ ^ 2 = AO ^ 2 – ОВ ^ 2;

ОВ ^ 2 = 82 ^ 2 – 18 ^ 2;

ОВ ^ 2 = 6724 – 324 = 6400;

OB = √6400;

OB = 80.

Answer: The radius of the circle is 80.