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

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 .

That means is a right triangle where .

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

We know by given that

, becaus it's the radius.

Using Pythagorean Theorem

Solving for

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

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation: