Chapter 11.4, Problem 52SPR

To determine

To find: The identification of the arc as major arc, minor arc, semicircle of the circle and then find its measure.

Answer to Problem 52SPR

The arc is minor and its value is $m\stackrel{⌢}{EB}=90$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The line $\overline{EC},\overline{AB}$ are the diameter.

Calculation:

The minor arc is the arc whose point is on the interior of the central angle.

The major arc is the arc whose points is on the exterior of the central angle.

If the end point of the arc lie on the diameter, then the arc is the semicircle.

The arc $\stackrel{⌢}{EB}$ is the shorter arc connecting to the points E and B on $\odot O$ .

Since, $\angle EOB$ is the right angle then by the definition of the right angle such that $m\angle EOB=90°$ . The definition of the minor arc shows that $\stackrel{⌢}{EB}$ is a minor arc and $\begin{array}{c}m\stackrel{⌢}{EB}=m\angle EOB\\ =90\end{array}$