Chord Practice

Front

What is a chord in a circle?

Back

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

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between a chord and a diameter?

Back

A diameter is the longest chord in a circle, passing through the center.

Front

If two chords intersect inside a circle, how do you find the lengths of the segments?

Back

Use the intersecting chords theorem: If two chords AB and CD intersect at point E, then AE * EB = CE * ED.

Tags

CCSS.HSG.C.A.2

Front

What is the formula for the area of a sector of a circle?

Back

Area of sector = (θ/360) * π * r², where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

How do you calculate the distance from the center of a circle to a chord?

Back

Use the formula: d = √(r² - (c/2)²), where d is the distance, r is the radius, and c is the length of the chord.

Tags

CCSS.HSG.C.A.2

Front

What is the relationship between the radius and a chord that is perpendicular to the radius?

Back

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

Front

If the length of a chord is 10 and the radius of the circle is 6, what is the distance from the center to the chord?

Back

Distance = √(6² - (10/2)²) = √(36 - 25) = √11.

Tags

CCSS.HSG.C.A.2

Front

What is the definition of an arc in relation to a chord?

Back

An arc is a portion of the circumference of a circle that is defined by the endpoints of a chord.

Front

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

Back

Use the formula: θ = 2 * arcsin(c/2r), where c is the length of the chord and r is the radius.

Tags

CCSS.HSG.C.A.2