Chapter 11.4, Problem 51SPR

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 51SPR

The definition of the semicircle shows that ACB is the semicircle and $m\stackrel{⌢}{ACB}=180$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

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.

Then, arc ACB is the semicircle is the corresponding arc of the diameter AB.

Then, by the definition of the semicircle shows that ACB is the semicircle and $m\stackrel{⌢}{ACB}=180$ .