Length of an arc that subtends a central angle | Circles | Geometry | Khan Academy

TL;DR

The length of an arc in a circle can be found by taking the ratio of the central angle to the total angle measure of the circle and multiplying it by the circumference.

Transcript

I have a circle here whose circumference is 18 pi. So if we were to measure all the way around the circle, we would get 18 pi. And we also have a central angle here. So this is the center of the circle. And this central angle that I'm about to draw has a measure of 10 degrees. So this angle right over here is 10 degrees. And what I'm curious about ... Read More

Key Insights

• ⭕ The length of an arc in a circle can be calculated using the ratio of the central angle to the total angle measure of the circle.
• 🫠 The formula for finding the arc length is: arc length = (central angle/360 degrees) * circumference of the circle.
• 🫠 A larger central angle will result in a longer arc length.
• 💦 The formula works for both acute and obtuse angles in a circle.
• 🔺 The arc length can be found by multiplying the ratio of the central angle to the total angle measure by the circumference of the circle.
• 🫠 This formula assumes a perfect circle and that the arc lies within the circumference.
• 🫠 It is important to know the size of the central angle and the circumference of the circle to calculate the arc length accurately.

Questions & Answers

Q: How do you calculate the length of an arc in a circle?

To calculate the length of an arc, you can use the formula: arc length = (central angle/360 degrees) * circumference of the circle.

Q: Does the size of the central angle affect the length of the arc?

Yes, the length of the arc is directly proportional to the size of the central angle. A larger central angle will result in a longer arc length.

Q: Are there any limitations to using this formula?

This formula assumes that the circle is perfectly round and that the arc lies within the circumference. Additionally, it only applies to the parts of the circle that are covered by the arc.

Q: Can this formula be used for circles of any size?

Yes, the formula can be used for circles of any size, as long as the circumference and angle measurements are known.

Summary & Key Takeaways

• The length of an arc in a circle can be determined by using the ratio of the central angle to the total angle measure of the circle.

• To find the length of an arc, multiply the ratio by the circumference of the circle.

• This formula works for both acute and obtuse angles.