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?
+1975 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."
XY2 = 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!
