Segments in Circles

Front

What is a segment in a circle?

Back

A segment in a circle is a region bounded by a chord and the arc that it subtends.

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: Area = (r^2/2) * (θ - 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 segments in a circle?

Back

The radius of a circle is the distance from the center to any point on the circle, and it plays a crucial role in determining the lengths and areas of segments.

Front

What is the central angle in relation to a segment?

Back

The central angle is the angle formed at the center of the circle by two radii that connect to the endpoints of a chord.

Front

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

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

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

Back

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

Front

What is the formula for the circumference of a circle?

Back

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

Front

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

Back

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

Front

What is the relationship between the angles subtended by arcs and chords?

Back

The angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the remaining part of the circle.