Chapter 10.7, Problem 19PSB

a.

To determine

Find the radius of the larger circle.

Answer to Problem 19PSB

  $20$

Explanation of Solution

Given information:

Equilateral triangle PQR is inscribed in one circle and circumscribed about another circle. The circles are concentric. If the radius of the smaller circle is 10.

  

Calculation:

Consider the given figure,

Radius of larger circle is $OQ$ ,

  $\begin{array}{l}\sin 30°=\frac{10}{OQ}\\ OQ=\frac{10}{\sin 30°}=\frac{10}{0.5}=20\\ OQ=20\end{array}$

  

Hence, the radius of the larger circle is $20$ .

b.

To determine

Find the ratio of radius of both circles.

Answer to Problem 19PSB

  $\frac{1}{2}$

Explanation of Solution

Given information:

Equilateral triangle PQR is inscribed in one circle and circumscribed about another circle. The circles are concentric. If the radius of the smaller circle is 10.

  

Calculation:

Consider the given figure,

Ratio of both the radius is always half,

  $10/20=1/2$

Hence, the ratio of radius is $\frac{1}{2}$ .