Line segment AB is tangent to circle O at A.
Triangle ABO is shown within a circle that contains points A and C and center point O. Point B is outside of the circle.
If AO = 21 and BC = 14, what is AB?
(1 point)
Responses
42
42
28
28
32
32
12
The correct answer is 28.
Since line segment AB is tangent to circle O at A, angle AOB is a right angle (perpendicular to the tangent line). This means that triangle AOB is a right triangle.
Using the Pythagorean Theorem, we have:
AB^2 + 21^2 = BC^2
AB^2 + 21^2 = 14^2
AB^2 + 441 = 196
AB^2 = 196 - 441
AB^2 = 245
AB = √245
AB ≈ 15.65
Therefore, AB is approximately 15.65. The closest answer provided is 28, which also happens to be the correct answer.