Line AB touches a circle centered at point O and a radius of 7 cm at point A. Find OB if AB = 24 cm.

Line AB, which is tangent to the circle centered at point O, is perpendicular to the radius of the circle drawn to the tangent point, that is, to point A.

Obviously, segments AB and OA are perpendicular. Draw a segment OB and get a right-angled triangle with legs OA and AB and hypotenuse OB. We use the Pythagorean theorem:

OB ^ 2 = OA ^ 2 + AB ^ 2;

OB ^ 2 = 49 + 576;

OB ^ 2 = 625;

OB = 25 cm.