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 the sum of the radii of circle X and circle Y. Given radius of circle X is 8 and radius of circle Y is 10, so diameter $d=8 + 10+8 + 10=36$.

Step2: Find the radius of circle C

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$^{2}$