Segments in Circles

Front

What is a segment in a circle?

Back

A segment in a circle is a region bounded by a chord and the arc that it subtends.

Front

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

Back

The area of a circle segment can be calculated using the formula: Area = (r^2/2) * (θ - sin(θ)), where r is the radius and θ is the angle in radians.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between the angles formed by two intersecting chords in a circle?

Back

The angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Tags

CCSS.HSG.C.A.2

Front

How do you find the length of an arc in a circle?

Back

The length of an arc can be found using the formula: Arc Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between the angles formed by a tangent and a chord?

Back

The angle formed between a tangent and a chord through the point of contact is equal to the measure of the opposite arc.

Tags

CCSS.HSG.C.A.2

Front

What is a sector in a circle?

Back

A sector is a region of a circle bounded by two radii and the arc between them.

Front

What is the formula for the area of a sector?

Back

The area of a sector can be calculated using the formula: Area = (θ/360) * πr^2, where θ is the central angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between the lengths of two chords that intersect inside a circle?

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.

Tags

CCSS.HSG.C.A.2

Front

How do you find the measure of an inscribed angle?

Back

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

Tags

CCSS.HSG.C.A.2

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle can be calculated using the formula: C = 2πr, where r is the radius.

Tags

CCSS.7.G.B.4