Answer:
No
Step-by-step explanation:
A tangent to a circle is perpendicular to the radius of the circle drawn to the point of tangency.
If segment XY is a tangent, then X is the point of tangency.
ZX then is the radius drawn to the point of tangency.
For segment XY to be a tangent to the circle, it must be perpendicular to radius XZ. That would make triangle XYZ a right triangle with right angle X.
We can use the Pythagorean theorem to see if if X is a right angle.
a² + b² = c²
(XZ)² + (XY)² = (YZ)²
8² + 10² = (8 + 5)²
64 + 100 = 13²
164 = 169
Since the side lengths of the triangle do not make the equation true, the triangle is not a right triangle. Angle X is not a right angle, and segment XY is not a tangent to circle Z.
