Question

If ZY = 15 and WX = 10, what is the length of the radius of circle V?

Answer 1

The information of ZY = 15 also gives the value of YX. ZY is the radius of the greater circle inside the big circle. So we have that:

`\text{ZY = YX = 15}`

The radius of the circle that has the center on X (the big one) is the sum of ZY and YX. This value is also equal to UX! Therefore:

`UX\text{ = ZY + YX = 15+15=30}`

If UX is 30 and the question says that WX is 10, we can find the following equation:

`UW\text{ + WX = UX}`

Obs: UV = VW (radius of the circle). Then we can find UW using the equation above (UW is the diameter of the circle with center V).

`30\text{ = UW + 15}`
`UW\text{ = 30-15 = 15}`

The diameter of a circle is two times the radius. Thus:

`UW\text{ = 2}* Radius`

Then the radius of the circle V will be:

`\text{Radius = }(UW)/(2)=(15)/(2)=7.5`