Arcs Examples

In the figure below, A and B are on ⊙O and m∠AOB = 38°. Is arc AB a major arc, a minor arc, or a semicircle?

Since arc AB subtends a central angle of 38°, the measure of arc AB is 38°. Since the measure of arc AB is less than 180°, it's a minor arc. That means it can't get into clubs till its 21st birthday.

What is the circumference of a circle with radius 18 cm?

We have a formula relating circumference and radius. It's C = 2πr. Plugging in 18 for r, we get C = 2π(18) = 36π. So the exact circumference is 36π cm, or approximately 113.04 cm.

What is the length of an arc with measure 78° and radius 5 m?

We use our arc length formula, . All we have to do is plug in the values r = 5 and θ = 78° to solve for L.

The exact length of the arc is , or approximately 6.81 m.

What is the radius of an arc with measure 90° and length 31 cm?

We're still going to need our arc length formula, , but this time we are given the arc measure and length and are asked to find the radius.

So the exact radius would be  cm, or approximately 19.74 cm.

In the figure below, points A, B, and C are on ⊙O, m∠AOB = 80°, and m∠BOC = 120°. What's the measure of arc AC?

We need to use arc addition and the fact that there are 360 total degrees in a circle.

360° = mAB + mBC + mAC

360° = 80° + 120° + mAC

360° = 200° + mAC

mAC = 360° – 200° = 160°