Question

Answer.

Answer 1

I have a working answer of 6 for XT but I have to check and post my work.

Answer 2

If a tangent segment and a secant segment are drawn to a circle from an outside point, then the square of the tangent length is equal to the length of the entire secant segment times the length of its external segment.
(TZ) ^2 = (SZ) * (YZ)
6^2 = SZ * 4
SZ = 9
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SZ = SX + XY + YZ
9 = 3 + XY + 4
2 = XY
and then ...

Answer 3

mine was the wrong one...

Answer 4

If two chords intersect within a circle, the product of the lengths of the segments of one chord is equal to the product of those of the other chord.
SX * XY = WX * XT
3 *2 = 1 * XT
XT = 6

Answer 5

Check my work, please.

Answer 6

Absolutely correct. Thanks ^^