Review: Central, Inscribed Angle and Arc Length

Front

What is a central angle in a circle?

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

Define an inscribed angle.

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle.

Front

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

Back

The measure of a central angle is twice the measure of the inscribed angle that subtends the same arc.

Front

How do you calculate the arc length of a circle?

Back

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

Front

What is the formula for finding the circumference of a circle?

Back

Circumference = 2πr, where r is the radius of the circle.

Front

If the radius of a circle is 10 ft, what is the circumference?

Back

Circumference = 2π(10) = 20π ft ≈ 62.83 ft.

Front

What is the measure of an arc in degrees if the central angle is 180°?

Back

The measure of the arc is also 180°.

Front

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

Back

The central angle would measure 120°.

Front

What is the relationship between the length of an arc and the radius of the circle?

Back

The length of an arc is directly proportional to the radius of the circle; as the radius increases, the arc length increases.

Front

How do you find the length of an arc if the central angle is 90° and the radius is 5 m?

Back

Arc Length = (90/360) * 2π(5) = (1/4) * 10π = 2.5π m ≈ 7.85 m.