Circle Chords, Arcs, Central Angles, Inscribed Angles

Front

What is a chord in a circle?

Back

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

Front

Define an arc in the context of a circle.

Back

An arc is a portion of the circumference of a circle.

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that intersect the circle.

Front

What is an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint.

Front

How do you calculate the measure of an arc?

Back

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

Front

What is the relationship between a central angle and an inscribed angle that subtends the same arc?

Back

The inscribed angle is half the measure of the central angle.

Front

If the measure of a central angle is 60°, what is the measure of the inscribed angle subtending the same arc?

Back

30°.

Front

What is the formula for the length of a chord given the radius and the central angle?

Back

Length of chord = 2 * r * sin(θ/2), where r is the radius and θ is the central angle in radians.

Front

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

Back

Longer arcs correspond to longer chords.

Front

If two chords intersect inside a circle, how do you find the measure of the angles formed?

Back

The measure of each angle is equal to half the sum of the measures of the arcs intercepted by the angle.