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Summary

This video explains what an arc is in geometry, how it relates to a circle, and provides a formula for calculating its length. It covers the definition of an arc as a segment of a circle's circumference, the concept of a central angle, and walks through an example calculation of arc length.

Highlights

What is an Arc?00:00:02

An arc is a segment of a circle's circumference, defined by rotating a radius less than 360 degrees. It is bound by two endpoints.

Central Angle and Arc Length00:01:15

The central angle determines the length of an arc; a larger angle results in a longer arc. Arc length is the distance along the curved path of the arc, which is always longer than a straight line between its endpoints.

Formula for Arc Length00:01:46

The arc length (s) can be calculated using the formula s = (theta/360) * 2πr, where theta is the central angle in degrees and r is the radius of the circle. This formula represents a fraction of the circle's total circumference.

Example Calculation of Arc Length00:02:42

To calculate the arc length, substitute the given central angle (theta) and radius (r) into the formula. For example, with a 4 cm radius and a 36-degree central angle, the arc length is approximately 2.51 cm.

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