G.11b Circle Segments

Front

What is a circle segment?

Back

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

Front

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

Back

To find the length of a chord, you can use the formula: L = 2 * r * sin(θ/2), where r is the radius and θ is the central angle in radians.

Front

What is the formula for the area of a circle segment?

Back

The area of a circle segment can be calculated 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 length of a chord?

Back

The length of a chord decreases as the angle subtended by the chord at the center of the circle decreases, given a constant radius.

Front

How do you calculate the perimeter of a polygon formed by circle segments?

Back

To calculate the perimeter, sum the lengths of all the sides, including the lengths of the chords and the arcs.

Front

What is the central angle of a circle segment?

Back

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

Front

How do you find the area of a sector of a circle?

Back

The area of a sector can be found using the formula: A = (θ/360) * π * r^2, where θ is the central angle in degrees and r is the radius.

Front

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

Back

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

Front

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

Back

The length of an arc can be calculated using the formula: L = (θ/360) * 2 * π * r, where θ is the central angle in degrees and r is the radius.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is given by the formula: C = 2 * π * r, where r is the radius.