segment lengths in 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 connecting the endpoints of the chord.

Front

What is the formula for the length of a chord in a circle?

Back

The length of a chord can be calculated using the formula: L = 2 * r * sin(θ/2), where r is the radius and θ is the central angle in radians.

Front

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

Back

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

Front

What is the relationship between the radius and the segment length in a circle?

Back

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

Front

What is the central angle in relation to a segment?

Back

The central angle is the angle subtended at the center of the circle by the endpoints of the segment.

Front

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

Back

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

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula: A = π * r^2, where r is the radius.

Front

What is the difference between a sector and a segment in a circle?

Back

A sector is the area enclosed by two radii and the arc between them, while a segment is the area enclosed by a chord and the arc.

Front

How do you find the angle subtended by a chord at the center of the circle?

Back

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

Front

What is the significance of the diameter in relation to segments?

Back

The diameter divides the circle into two equal segments, and any segment formed by a chord that is a diameter is a semicircle.