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

If ZY 15 And WX 10 What Is The Length Of The Radius Of Circle V class=

Sagot :

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]

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