line segment wx is the radius of circle x, and line segment zy is the radius of circle y. points w, x, c, y…

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

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

Answer

Explanation:

Step1: Find the diameter of circle C

The diameter of circle C is the sum of the diameters of circle X and circle Y. The diameter of circle X is $2\times8 = 16$ (since radius is 8), and the diameter of circle Y is $2\times10=20$. So the diameter of circle C is $16 + 20=36$.

Step2: Find the radius of circle C

The radius $r$ of circle C is half of its diameter. 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, we get $A=\pi\times18^{2}=324\pi$.

Answer:

$324\pi$ units$^{2}$