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: Area = (r^2/2) * (θ - sin(θ)), where r is the radius and θ is the angle in radians.

Front

What is the relationship between a tangent and a radius at the point of tangency?

Back

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Front

If two chords intersect inside a circle, how do you find the lengths of the segments?

Back

The products of the lengths of the segments of each chord are equal. If AB and CD are chords intersecting at point E, then AE * EB = CE * ED.

Front

What is the angle subtended by an arc at the center of the circle?

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.

Front

How do you find the length of a tangent segment from a point outside the circle?

Back

The length of the tangent segment from a point outside the circle to the point of tangency can be found using the formula: Length = √(d^2 - r^2), where d is the distance from the point to the center of the circle and r is the radius.

Front

What is the relationship between the angles formed by two intersecting chords?

Back

The measure of the angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

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

What is the definition of a chord in a circle?

Back

A chord is a line segment whose endpoints lie on the circle.

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/360) * πr^2, where θ is the angle in degrees and r is the radius.