Segment Lengths (Circles)

Front

What is the definition of a segment in a circle?

Back

A segment in a circle is the region bounded by a chord and the arc that connects the endpoints of the chord.

Front

What is the formula to find the length of a segment in a circle?

Back

The length of a segment can be found using the formula: Length = r^2 * θ - (1/2) * r^2 * sin(θ), where r is the radius and θ is the angle in radians.

Front

How do you find the length of a chord in a circle?

Back

The length of a chord can be found using the formula: L = 2 * r * sin(θ/2), where r is the radius and θ is the angle subtended by the chord at the center.

Front

What is the relationship between the radius and the segment length?

Back

The length of a segment is directly related to the radius of the circle; as the radius increases, the segment length can also increase.

Front

What is the definition of a sector in a circle?

Back

A sector is the region enclosed by two radii and the arc between them.

Front

What is the formula for the area of a sector?

Back

The area of a sector can be calculated using the formula: Area = (θ/2π) * πr^2 = (θ/2) * r^2, where θ is in radians.

Front

How do you calculate the area of a segment in a circle?

Back

The area of a segment can be calculated by subtracting the area of the triangle formed by the radii and the chord from the area of the sector.

Front

What is the definition of an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

Front

How do you find the length of an arc?

Back

The length of an arc can be found using the formula: Arc Length = r * θ, where r is the radius and θ is the angle in radians.

Front

What is the relationship between the angle and the arc length?

Back

The arc length is directly proportional to the angle; as the angle increases, the arc length also increases.