Chapter 13.6, Problem 17PSC

To determine

To find: The area of the given circle.

Answer to Problem 17PSC

The area of the circle is $17\pi$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

From the give figure, the centre of the circle is at equal distance from the point $\left(0,0\right)$ and $\left(8,0\right)$ . Thus, the centre is at the perpendicular bisector of $x=4$ , thus the centre points are $\left(4,y\right)$ .

Then, the y coordinate of the centre is obtained as

  $\begin{array}{l}\sqrt{{\left(4-5\right)}^2+{\left(y-3\right)}^2}=\sqrt{4^2+y^2}\\ {\left(4-5\right)}^2+{\left(y-3\right)}^2=4^2+y^2\\ 1+y^2-6y+9=16+y^2\\ y=-1\end{array}$

Then, the radius of the circle is,

  $\begin{array}{c}r=\sqrt{{\left(4-0\right)}^2+{\left(-1+0\right)}^2}\\ =\sqrt{17}\end{array}$

Thus, the area of the circle is,

  $\begin{array}{c}A=r^2\pi \\ ={\left(\sqrt{17}\right)}^2\pi \\ =17\pi \end{array}$