#10.3 Using Chords

Front

What is a chord in geometry?

Back

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

Front

What is the relationship between the radius and a chord?

Back

The perpendicular from the center of the circle to a chord bisects the chord.

Front

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

Back

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

Front

What is the significance of a diameter in relation to chords?

Back

A diameter is the longest chord of a circle.

Front

If two chords intersect inside a circle, what is the relationship between the segments?

Back

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

Front

What is the formula for the area of a sector formed by a chord?

Back

Area = (θ/360) * πr², where θ is the angle in degrees and r is the radius.

Front

How do you determine if a chord is longer than another chord?

Back

A chord is longer if it is closer to the center of the circle.

Front

What is the relationship between the angles subtended by chords at the center and on the circumference?

Back

The angle subtended at the center is twice the angle subtended at the circumference.

Front

What is a secant line?

Back

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

Front

How can you find the length of a chord using the central angle?

Back

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