Answer:
15 units
Step-by-step explanation:
In the image attached you can notice that line ZY is tangent at point Y.
Remember that the radius is always perpendicular to tangents, by definition, that means [tex]XY \perp ZY[/tex].
That means [tex]\triangle XYZ[/tex] is a right triangle where [tex]\angle Y = 90\°[/tex].
All these facts are deducted form having ZY as a tangent.
We know by given that
[tex]XZ=8+9=17[/tex]
[tex]XY=8[/tex], becaus it's the radius.
Using Pythagorean Theorem
[tex]17^{2} =8^{2}+ZY^{2}[/tex]
Solving for [tex]ZY[/tex]
[tex]ZY=\sqrt{17^{2} -8^{2} } \\ZY=\sqrt{289-64}\\ ZY=\sqrt{225}\\ ZY=15[/tex]
Therefore, the length of ZY must be 15 units to be tangent to circle X.
