Chapter 9.6, Problem 28WE

To determine

To find: the ratio of $x:y$ .

Answer to Problem 28WE

The ratio is $\frac{x}{y}=\frac{2}{1}$ .

Explanation of Solution

Given Information:

Given figure,

  

Calculation:

Figure shows a circle center $O$ , where an angle with measurement $2n^0$ is formed in the minor segment of arc with measurement $x^0$ and an angle of measurement $n^0$ is formed by intersection of two secants and corresponding arcs of $x^0$ and $y^0$ .

As from the figure,

  $\begin{array}{c}2n=\frac{1}{2}x\\ 2n=\frac{x}{2}\\ 4n=x\end{array}$

And also,

  $n=\frac{1}{2}\left(x-y\right)$

Put the value of $n$ in first equation,

  $\begin{array}{c}4n=x\\ 4\left(\frac{1}{2}\left(x-y\right)\right)=x\\ 2x-2y=x\end{array}$

Subtract $2x$ on both sides to get,

  $\begin{array}{c}2x-2y-2x=x-2x\\ -2y=-x\\ 2y=x\\ \frac{x}{y}=\frac{2}{1}\end{array}$

Hence, the ratio is $\frac{x}{y}=\frac{2}{1}$ .