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 \(X\) is \(2\times8 = 16\), and the diameter of circle \(Y\) is \(2\times10=20\).
The length of \(WZ\) (diameter of circle \(C\)) is \(2\times8 + 2\times10=16 + 20 = 36\)

Step2: Find the radius of circle \(C\)

Since the diameter \(d = 36\), then the radius \(r=\frac{d}{2}=\frac{36}{2}=18\)

Step3: Calculate the area of circle \(C\)

The area formula of a circle is \(A=\pi r^{2}\). Substitute \(r = 18\) into the formula: \(A=\pi\times18^{2}=324\pi\)

Answer:

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