a A circular arc is a portion of a circle and its measure is the same as the measure of its central angle.
B
b A circular arc is a portion of a circle and its measure is the same as the measure of its central angle.
C
c A circular arc is a portion of a circle and its measure is the same as the measure of its central angle.
D
d A circular arc is a portion of a circle and its measure is the same as the measure of its central angle.
A
aExample Circular Arc:
B
bExample Circular Arc:
C
cExample Circular Arc:
D
dExample Circular Arc:
Practice makes perfect
a We are asked to draw a circular arc with the given measures using dynamic geometry software. Note that a circular arc is a portion of a circle. The measure of a circular arc is the same as the measure of its central angle.
In ⊙ O, the measure of AB is equal to the measure of ∠ AOB. Now, to draw a circular arc measuring 30^(∘), we will first draw a central angle whose measure is 30 ^(∘).
The intercepted arc AB of the central angle ∠ AOB is a circular arc with measure 30^(∘).
Note that there are infinitely many circular arcs with measure 30 ^(∘). This is just one example.
b Next, we will draw a circular arc whose measure is 45 ^(∘). Let's first draw its central angle.
Since its circular arc is AB, we have a circular arc measuring 45^(∘). Again, this is just one of the infinitely many circular arcs with measure 45^(∘).
c In this part, proceeding in the same way, we will draw a central angle with measure 60^(∘).
Therefore, the measure of AB is 60^(∘).
d Finally, we are asked draw a circular arc with a measure of 90^(∘).
As we can see, the measure of ∠ AOB is 90 ^(∘). This means that the measure of its circular arc AB is also 90^(∘).
