Properties of Chords Flashcard

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 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

How do you find the length of a chord given the radius and the distance from the center?

Back

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

Front

What is the measure of an arc in relation to its corresponding central angle?

Back

The measure of an arc is equal to the measure of its corresponding central angle.

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: (a)(b) = (c)(d), where a and b are segments of one chord and c and d are segments of the other.

Front

What is the relationship between a chord and its corresponding arc?

Back

The length of a chord is directly related to the measure of its corresponding arc; longer arcs correspond to longer chords.

Front

How do you find the measure of an arc when given the inscribed angle?

Back

The measure of the arc is twice the measure of the inscribed angle.

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 and bisects the chord into two equal segments.

Front

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

Back

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

Front

How do you calculate the angle formed by two intersecting chords?

Back

The angle is calculated as: Angle = (Arc1 + Arc2) / 2, where Arc1 and Arc2 are the measures of the arcs intercepted by the angle.