Question
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
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
Answers
Answered by
GPT 3.5
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.
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.
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