Chords and Arcs (Sec 10.3)

Front

What is a chord in a circle?

Back

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

Front

What is an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

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 relationship between the central angle and the arc length?

Back

The arc length is directly proportional to the central angle. Arc length = (θ/360) * 2πr, where θ is the angle in degrees.

Front

How do you calculate the measure of an inscribed angle?

Back

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

Front

What is the formula for finding the measure of an arc?

Back

The measure of an arc is equal to the measure of the central angle that subtends it.

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 the radius and the chord length?

Back

As the distance from the center of the circle to the chord increases, the length of the chord decreases.

Front

How do you find the arc measure for a given angle?

Back

The arc measure can be found using the formula: Arc measure = (θ/360) * 2πr, where θ is the angle in degrees.

Front

What is the difference between a major arc and a minor arc?

Back

A minor arc is less than 180 degrees, while a major arc is greater than 180 degrees.