Practice: 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

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

Back

The area of a circle segment can be calculated using the formula: \( A = \frac{r^2}{2} (\theta - \sin(\theta)) \), where \( r \) is the radius and \( \theta \) is the central angle in radians.

Front

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

Back

The relationship is given by the formula: \( c = 2r \sin(\frac{\theta}{2}) \), where \( c \) is the chord length, \( r \) is the radius, and \( \theta \) is the angle in radians.

Front

How do you find the height of a circle segment?

Back

The height of a circle segment can be found using the formula: \( h = r - \sqrt{r^2 - (\frac{c}{2})^2} \), where \( h \) is the height, \( r \) is the radius, and \( c \) is the chord length.

Front

What is the central angle of a circle segment?

Back

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

Front

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

Back

The length of an arc can be calculated using the formula: \( L = r\theta \), where \( L \) is the arc length, \( r \) is the radius, and \( \theta \) is the angle in radians.

Front

What is the relationship between the area of a circle segment and the area of the triangle formed by the chord and the radii?

Back

The area of the circle segment is equal to the area of the triangle formed by the chord and the two radii plus the area of the sector minus the area of the triangle.

Front

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

Back

The area of a sector can be calculated using the formula: \( A = \frac{1}{2} r^2 \theta \), where \( r \) is the radius and \( \theta \) is the angle in radians.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: \( radians = degrees \times \frac{\pi}{180} \).

Front

What is the significance of the chord in a circle segment?

Back

The chord is significant as it defines the boundary of the circle segment and is used to calculate various properties such as area and height.