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:
[tex]\text{ZY = YX = 15}[/tex]
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:
[tex]UX\text{ = ZY + YX = 15+15=30}[/tex]
If UX is 30 and the question says that WX is 10, we can find the following equation:
[tex]UW\text{ + WX = UX}[/tex]
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).
[tex]30\text{ = UW + 15}[/tex][tex]UW\text{ = 30-15 = 15}[/tex]
The diameter of a circle is two times the radius. Thus:
[tex]UW\text{ = 2}\times Radius[/tex]
Then the radius of the circle V will be:
[tex]\text{Radius = }\frac{UW}{2}=\frac{15}{2}=7.5[/tex]
