Chord Theorems

Front

What is a Chord in a Circle?

Back

A chord is a line segment with both endpoints on the circle.

Front

What is the definition of a Diameter?

Back

A diameter is a chord that passes through the center of the circle, dividing it into two equal halves.

Front

What is the relationship between a chord and its arc?

Back

The arc is the part of the circle that lies between the endpoints of the chord.

Front

What is the Chord Theorem?

Back

The Chord Theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal.

Front

How do you find the length of a chord given the radius and the angle subtended at the center?

Back

Use the formula: Length of chord = 2 * r * sin(θ/2), where r is the radius and θ is the angle in radians.

Front

What is the Perpendicular Bisector Theorem for Chords?

Back

The perpendicular bisector of a chord passes through the center of the circle.

Front

What is the relationship between two chords that are equidistant from the center of the circle?

Back

If two chords are equidistant from the center, they are equal in length.

Front

What is the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

How do you calculate the measure of an arc?

Back

The measure of an arc can be calculated using the formula: Arc measure = (Central angle/360) * Circumference of the circle.

Front

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

Back

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