Central Angles & Arcs

Front

What is a central angle?

Back

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

Front

How do you calculate the measure of a central angle in degrees?

Back

The measure of a central angle can be calculated using the formula: (Arc Length / Radius) * (180/π) if the arc length is known.

Front

What is the relationship between a central angle and its intercepted arc?

Back

The measure of a central angle is equal to the measure of its intercepted arc.

Front

Define an arc in the context of a circle.

Back

An arc is a portion of the circumference of a circle, defined by two endpoints on the circle.

Front

What is the formula for the length of an arc?

Back

The length of an arc can be calculated using the formula: Arc Length = (Central Angle in Radians / 2π) * Circumference of the Circle.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, multiply the degree measure by π/180.

Front

What is the formula for the circumference of a circle?

Back

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

Front

What is the relationship between the radius and the arc length?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases for a given central angle.

Front

How do you find the measure of an inscribed angle?

Back

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

Front

What is the difference between a minor arc and a major arc?

Back

A minor arc is an arc that is less than 180 degrees, while a major arc is an arc that is greater than 180 degrees.