Question

What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

Answer 1

Not sure but i put 17 units

Answer 2

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 $XY \perp ZY$.

That means $\triangle XYZ$ is a right triangle where $\angle Y = 90\°$.

All these facts are deducted form having ZY as a tangent.

We know by given that

$XZ=8+9=17$

$XY=8$, becaus it's the radius.

Using Pythagorean Theorem

$17^{2} =8^{2}+ZY^{2}$

Solving for $ZY$

$ZY=\sqrt{17^{2} -8^{2} } \\ZY=\sqrt{289-64}\\ ZY=\sqrt{225}\\ ZY=15$

Therefore, the length of ZY must be 15 units to be tangent to circle X.