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
12
12
42
42
32
32
28
We can use the Pythagorean Theorem to find AB.
AO = 21, BC = 14, so CO = BC/2 = 7.
Using the Pythagorean Theorem in triangle ACO:
AC^2 = AO^2 + CO^2
AC^2 = 21^2 + 7^2
AC^2 = 441 + 49
AC^2 = 490
AC = sqrt(490)
AC = 7*sqrt(10)
Since AB is a tangent to the circle, triangle ABC is right-angled triangle, so we can find AB:
AB^2 = AC^2 + BC^2
AB^2 = (7*sqrt(10))^2 + 14^2
AB^2 = 490 + 196
AB^2 = 686
AB = sqrt(686)
AB = sqrt(49*14)
AB = 7*sqrt(14)
AB = 7*sqrt(14)
Therefore, AB = 7*sqrt(14) = 28.
The correct answer is 28.