Question

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

14 units
15 units
16 units
17 units

Answer 1

15 units

Explanation:

The guy above me has got it right! :D

Answer 2

15 units

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=√(289-64)\\ ZY=√(225)\\ ZY=15`

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