Question

ab is tangent circle O at B find the length of the radius r for ab=10 and ao= 22.3 round to the nearest tenth necessary

19.6
19.9
24.4
17.8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we can use the Pythagorean Theorem because AB is a tangent to circle O at B, making AB perpendicular to the radius OA.

First, we need to find the length of OB, which is equal to the radius of circle O. We can do this by using the Pythagorean Theorem:

OA^2 = OB^2 + AB^2
(22.3)^2 = OB^2 + (10)^2
497.29 = OB^2 + 100
OB^2 = 397.29
OB = sqrt(397.29)
OB ≈ 19.9

Therefore, the length of the radius r, which is OB, is approximately 19.9. So, the closest answer choice is 19.9.

Therefore, the length of the radius r is 19.9.