Chapter 9.3, Problem 10PSA

To determine

To find: Measure the arc $RH$ i.e. $m(\stackrel{⌢}{RH)}$ .

Answer to Problem 10PSA

The measure of arc $RH\text{ is }\frac{\text{π}}{4}\left(\stackrel{⌢}{RH}\right)$

Explanation of Solution

Given information :

  $\angle RGH\text{ = 90}°$

  $RH$ is the diameter of the circle.

Formula used :

  $\text{Measure of arc }=\frac{\text{Arc angle}}{{360}^{\text{o}}}\times \text{Circumference}$

Note- In this question, we are measuring to arc length.

Calculation :

  $\begin{array}{l}\text{Measure of arc }RH=\frac{\angle RGH}{{360}^{\text{o}}}\times \text{Circumference}\\ =\frac{{90}^{\text{o}}}{{360}^{\text{o}}}\times 2\text{π}r\text{ (Circumference}=2\pi r)\\ =\frac{1}{4}\times \text{π}·d\\ \text{=}\frac{\pi }{4}\left(\stackrel{⌢}{RH}\right)\end{array}$

Where $\begin{array}{l}RH=\text{Diameter }\\ \Rightarrow d=2r\end{array}$