Chapter 9.3, Problem 1CE

To determine

To define: using the diagram, state required names.

Answer to Problem 1CE

The required names are:

a. Four central angles: $\measuredangle DOC,\measuredangle COB,\text{}\measuredangle AOB,\measuredangle AOD$ .

b. A semicircle:  $\stackrel{⌢}{ADO}$

c. Two minor arcs:  $\stackrel{⌢}{AB}and\stackrel{⌢}{CD}$ .

d. Two major arc: $\stackrel{⌢}{ADC}and\stackrel{⌢}{BDA}$ .

Explanation of Solution

Given information: Consider the given figure as shown in the book as reference.

a. Central angle of a circle is an angle with its vertex at the center of the circle.

By analyzing the diagram, four central angles are: $\measuredangle DOC,\measuredangle COB,\text{}\measuredangle AOB,\measuredangle AOD$ .

b. If two points are endpoints of diameter, then two arcs are called semicircles.

By analyzing the diagram, a semicircle is $\stackrel{⌢}{ADO}$ .

c. Minor arc is the arc which is smaller than a semicircle.

By analyzing the diagram, two minor arcs are $\stackrel{⌢}{AB}and\stackrel{⌢}{CD}$ .

d. Major arc is arc that is larger than semicircle.

By analyzing the diagram, two major arcs are $\stackrel{⌢}{ADC}and\stackrel{⌢}{BDA}$ .