Question
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
Answers
GPT 3.5
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
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