1. 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. (1 point) Responses 15.8 15.8 8.4 8.4 12.3 12.3 19.6

Answer 1

To find the length of the radius (r), we can use the property that a line tangent to a circle is perpendicular to the radius at the point of tangency. This means that triangle ABO is a right triangle.

Using the Pythagorean theorem: (AO)^2 = (AB)^2 + (BO)^2
(12.3)^2 = (9)^2 + (r)^2
151.29 = 81 + r^2
r^2 = 70.29
r = sqrt(70.29)
r ≈ 8.4 (rounded to the nearest tenth)

Therefore, the length of the radius is approximately 8.4. The correct answer is:

8.4