Chapter 10.5, Problem 20PSB

To determine

To Find : The angle formed by the tangents.

Answer to Problem 20PSB

  $\text{45°}$

Explanation of Solution

Given information :

  $\text{Major }\stackrel{⌢}{\text{AB}}=\frac{5}{3}\text{ minor}\stackrel{⌢}{\text{AB}}$

Formula Used: The angle between two tangents is equal to half the difference of the enclosed areas.

  $\begin{array}{l}\text{minor }\stackrel{⌢}{\text{AB}}+\text{ major }\stackrel{⌢}{\text{AB}}=360°\\ \text{minor }\stackrel{⌢}{\text{AB}}+\frac{5}{3}\text{ major }\stackrel{⌢}{\text{AB}}=360°\\ \frac{8}{3}\text{ minor }\stackrel{⌢}{\text{AB}}=360°\\ \text{minor }\stackrel{⌢}{\text{AB}}=135°\\ \text{minor }\stackrel{⌢}{\text{AB}}=225°\\ \text{Now,}\theta =\frac{1}{2}(\text{major }\stackrel{⌢}{\text{AB}}-\text{minor }\stackrel{⌢}{\text{AB}})\\ \theta =\frac{1}{2}(225°-135°)\\ \theta =\frac{1}{2}90°\\ \theta =45°\end{array}$