Arcs & Chords

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 diameter and the radius of a circle?

Back

The diameter is twice the length of the radius.

Tags

CCSS.7.G.B.4

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 perpendicular bisector of a chord?

Back

The perpendicular bisector of a chord passes through the center of the circle and divides the chord into two equal parts.

Front

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

Back

Two chords that are equidistant from the center of a circle are equal in length.

Tags

CCSS.HSG.C.A.2

Front

How do you calculate 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

What is the arc length of a circle?

Back

Arc length = (θ/360) * 2 * π * r, where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

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

Back

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

Tags

CCSS.HSG.C.A.2

Front

What is a semicircle?

Back

A semicircle is an arc that represents half of a circle, subtended by a diameter.

Front

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

Back

Use the formula: Angle = 2 * arcsin(length of chord / (2 * radius)).

Tags

CCSS.HSG.C.A.2