Tangent AB (B-tangency point) and secant AO are drawn to the circle centered at point O.

Tangent AB (B-tangency point) and secant AO are drawn to the circle centered at point O. Find the length of the section of the secant AO if AB = 40mm, OB = 30mm.

Since the straight line AB is tangent to the circle, and the segment OB is the radius drawn to the point of tangency, the straight line AB and OB will be perpendicular to each other. Therefore, our ABO triangle is right-angled and the angle B = 90 degrees.
The segments AB and OB of the leg of the triangle, and the segment AO is its hypotenuse
By the Pythagorean theorem:
AO ^ 2 = AB ^ 2 + OB ^ 2
we get: AO ^ 2 = 900 + 1600 = 2500 mm ^ 2
or AO = 50 mm