Segment AB is tangent to circle O at B. The diagram is not drawn to scale. If AB = 9 and AO = 12.3, what is the length of the radius (r)? Round your answer to the nearest tenth.

Answer 1

First, we know that the radius (r) is perpendicular to the tangent at the point of tangency. Therefore, ΔOAB is a right triangle with O being the center of the circle.

Using the Pythagorean theorem, we can find the length of the radius:

r^2 = AO^2 - AB^2
r^2 = 12.3^2 - 9^2
r^2 = 151.29 - 81
r^2 = 70.29
r ≈ √70.29
r ≈ 8.4

Therefore, the length of the radius is approximately 8.4.