Geo Arcs and Chords

Front

What is the relationship between congruent arcs and chords in a circle?

Back

In a circle (or congruent circles), congruent arcs have congruent chords.

Tags

CCSS.8.G.A.2

Front

How do you find the length of a chord given the radius and the angle subtended at the center?

Back

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

Tags

CCSS.HSG.C.A.2

Front

What is the measure of a central angle in a circle?

Back

The measure of a central angle is equal to the measure of the arc it intercepts.

Tags

CCSS.4.MD.C.5B

CCSS.HSG.CO.A.1

Front

How do you calculate the measure of an arc given the central angle?

Back

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

Tags

CCSS.HSG.C.B.5

Front

What is the formula for the length of an arc?

Back

Arc length = (θ/360) * 2 * π * r, 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 two intersecting chords?

Back

The measure of the angle formed by two intersecting chords is equal to the average of the measures of the arcs intercepted by the angle.

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 significance of the radius in relation to chords and arcs?

Back

The radius is crucial for calculating the lengths of chords and arcs, as well as determining relationships between angles and arcs.

Front

How can you determine if two chords are congruent?

Back

Two chords are congruent if they are equidistant from the center of the circle.

Front

What is the relationship between the lengths of chords and their corresponding arcs?

Back

In a circle, longer chords subtend larger arcs, and shorter chords subtend smaller arcs.

Tags

CCSS.HSG.C.A.2