Let XY be a tangent to a circle, and let be a XBA secant of the circle, as shown below. If AX = 16 and XY = 8, then what is AB?

Guest May 23, 2022

#1**+1 **

I actually found a similar question back in 2020 that Melody answered, so I'm just going to reuse her method (thank you Melody!)

You can use the Tangent-Secant Power Theorem for this problem.

"If a tangent and a secant intersect in the exterior of a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant and its external secant segment."

XY^{2} = XB(AX)

Plug in your numbers

(8)^{2 }= XB(16)

Simplify

64 = 16XB

Divide by 16 on both sides

4 = XB

Now, to find AB, you subtract XB from AX

AB = 16 - 4

AB = 12

Hope that helps!

saseflower May 23, 2022