Chapter 8.2, Problem 5PSA

To determine

To calculate:The given sides on the similar triangles inscribed the circle

Answer to Problem 5PSA

The required sides are: 6 and 9 units.

Explanation of Solution

Given information

Two circles with centers O & P

  $\Delta \text{AOB }\sim \Delta \text{RPS}$

OA = 2, AB = 3, PR = 6

Formula used

Ratios of corresponding sides are equivalent

Radii of circle are equal

Calculation

Given,

OA = OB = 2 units, radii of circle with center O

PS = PR = 6 units

AB = 3 units

Now,

  $\begin{array}{l}\frac{\text{PS}}{\text{PR}}=\frac{\text{OB}}{\text{OA}}\\ \Rightarrow \text{PS=PR}\text{}\times \frac{\text{OB}}{\text{OA}}=6\times \frac{2}{2}=6\text{ units}\end{array}$

Now for RS, we have

  $\begin{array}{l}\frac{\text{RS}}{\text{PR}}=\frac{\text{AB}}{\text{OA}}\\ \Rightarrow \text{RS=PR}\times \frac{\text{AB}}{\text{OA}}=6\times \frac{3}{2}=9\text{ units}\end{array}$