Honors Geometry - Theorems About Chords

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 relationship between the lengths of two chords that intersect inside a circle?

Back

The products of the lengths of the segments of each chord are equal.

Front

If two chords are equal in length, what can be said about their distances from the center of the circle?

Back

The chords are equidistant from the center of the circle.

Front

What is the formula for finding the length of a chord given the radius and the distance from the center to the chord?

Back

Length of chord = 2 * √(r² - d²), where r is the radius and d is the distance from the center.

Front

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

Back

The angle subtended at the center is twice the angle subtended at any point on the circumference.

Front

What is the relationship between a diameter and a chord?

Back

A diameter is the longest chord in a circle.

Front

If a chord is perpendicular to a radius at its endpoint, what can be said about the chord?

Back

The chord is bisected by the radius.

Front

What is the significance of the perpendicular bisector of a chord?

Back

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

Front

How do you calculate the length of a chord if you know the central angle?

Back

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

Front

What is the relationship between the arcs subtended by two equal chords?

Back

The arcs subtended by equal chords are also equal.