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 1296π units² 324π units²

Explanation:

Step1: Find the diameter of circle C

The diameter of circle C is \(WZ\). The radius of circle \(X\) is \(WX = 8\), so the diameter of circle \(X\) is \(2\times8=16\). The radius of circle \(Y\) is \(ZY = 10\), so the diameter of circle \(Y\) is \(2\times10 = 20\). Then \(WZ=16 + 20=36\).

Step2: Find the radius of circle C

Since the diameter \(d = 36\), 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, we get \(A=\pi\times18^{2}=324\pi\).

Answer:

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