Answer:
XY is tangent to circle Z
Explanation:
You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.
Pythagorean relation
If the triangle XYZ is a right triangle, then we have ...
XY² +XZ² = YZ²
3.6² +2.7² = (1.8 +2.7)²
12.96 +7.29 = 20.25 . . . . . true
Segment XY is a tangent.
Secant relation
If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...
3.6² = (1.8)(7.2) . . . . . true
This means XY is a tangent.