Question

line segment wx is the radius of circle x, and line segment zy is the radius of circle y. points w, x, c, y, and z are all on line segment wz. what is the area of circle c, which passes though points w and z? 81π units² 164π units² 324π units² 1296π units²

Explanation:

Step1: Find the diameter of circle C

The diameter of circle C is \(WZ\). Since \(WX = 8\) (radius of circle X) and \(ZY=10\) (radius of circle Y), then \(WZ=2\times8 + 2\times10\).

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Step2: Find the radius of circle C

The radius \(r\) of circle C is \(\frac{WZ}{2}\). So \(r=\frac{36}{2}=18\).

Step3: Calculate the area of circle C

The area formula of a circle is \(A=\pi r^{2}\). Substitute \(r = 18\) into the formula:

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Answer:

\(324\pi\) units\(^{2}\)