Segment Of A Circle
A segment of a circle is the region enclosed between a chord and its corresponding arc. A chord divides the circular region into two parts: the smaller region is called the minor segment, and the larger region is called the major segment.
Key Concepts
The minor segment is bounded by a chord and the minor arc, making its area smaller than a semicircle.
The major segment is bounded by the same chord and the major arc, making its area larger than a semicircle.
To calculate the area of a segment, you must first find the area of the corresponding sector and then subtract the area of the triangle formed by the chord and the two radii.
Formula & Equation
r \text{ is the radius of the circle, and } \theta \text{ is the central angle subtended by the chord in degrees.}
Common Misconceptions
Myth: Students often confuse a segment of a circle with a sector of a circle.
Fact: A sector is shaped like a slice of pie, bounded by two radii and an arc. A segment is bounded by a single chord and an arc, resembling a piece cut off from the edge of the circle.
Real World Applications
The cross-section of water flowing in a partially filled horizontal cylindrical pipe forms a segment of a circle.
A piece of a round flatbread or pizza cut by a single straight knife stroke that does not pass through the center.
Frequently Asked Questions
How do you calculate the area of a segment of a circle?
You calculate it by finding the area of the sector formed by the chord's endpoints and subtracting the area of the triangle formed by the radii and the chord.
What is the difference between a minor segment and a major segment?
A minor segment is the smaller area enclosed by a chord and a minor arc, while the major segment is the larger area enclosed by the same chord and the major arc.