Understanding Arc Length, Measure, Central Angle, Sector, Chord, and Tangent in Mathematics

Arc

In mathematics, an arc is a portion of a curve or a part of the circumference of a circle

In mathematics, an arc is a portion of a curve or a part of the circumference of a circle. It is characterized by two endpoints, also known as the arc’s terminal points. The arc is the path traced by a moving point on the curve or the circle.

Arc Length: The length of an arc is the measure of the distance along the curve between its two endpoints. It is usually represented by the Greek letter “s”. To calculate the arc length, you need to know the radius (r) of the circle and the central angle (θ) in radians or degrees that the arc subtends.

The formula for calculating the arc length is given by:
s = rθ

where s is the arc length, r is the radius, and θ is the central angle measured in radians.

Arc Measure: The measure of an arc is the size or the angular extent of the arc. It is usually given in degrees or radians. The measure of a whole circle is 360 degrees or 2π radians. The measure of a semicircle is 180 degrees or π radians.

Central Angle: The central angle is the angle formed by two radii of a circle that intercept or subtend the arc. It is also known as the arc’s angle measure. The central angle determines the size of the arc.

Sector: A sector is a region enclosed by two radii of a circle and the arc intercepted between them. It is essentially a “slice” of the circle. The sector is characterized by its central angle and its corresponding arc.

Chord: A chord is a line segment that connects two points on a curve, typically a circle. In the context of an arc, the chord refers to the straight line segment that connects the arc’s endpoints.

Tangent: A tangent is a straight line that touches a curve at only one point, without crossing or intersecting it. In the case of a circle, a tangent line intersects the circle at exactly one point, which is known as the point of tangency.

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