Congruent Chords and Arcs

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 congruent chords and their arcs?

Back

Congruent chords in a circle subtend congruent arcs.

Front

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

Back

Congruent chords are equidistant from the center of the circle.

Front

What is the measure of an arc if the corresponding chord is known to be congruent to another chord?

Back

The measures of the arcs corresponding to congruent chords are also congruent.

Front

If arc AB measures 96°, what is the measure of the arc subtended by a congruent chord?

Back

The measure of the arc subtended by a congruent chord is also 96°.

Front

What is a secant line?

Back

A secant line is a line that intersects a circle at two points.

Front

What is a tangent line?

Back

A tangent line is a line that touches a circle at exactly one point.

Front

If two chords intersect inside a circle, how can you find the measure of the angles formed?

Back

The measure of each angle is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

What is the formula for finding the length of a chord given the radius and the angle subtended at the center?

Back

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

Front

If the diameter of a circle is 10 cm, what is the length of a chord that is 6 cm from the center?

Back

The length of the chord can be found using the Pythagorean theorem: Length = 2 * √(r² - d²) = 2 * √(5² - 6²) = 8 cm.