Unit 6 Circles

Front

What is the definition of a radius in a circle?

Back

The radius of a circle is the distance from the center of the circle to any point on its circumference.

Front

What is the formula to calculate the arc length of a circle?

Back

The arc length (L) can be calculated using the formula: L = r * θ, where r is the radius and θ is the central angle in radians.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: radians = degrees × (π/180).

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 extend to the circumference.

Front

What is the relationship between the central angle and the arc length?

Back

The arc length is directly proportional to the central angle; as the angle increases, the arc length increases.

Front

If a circle has a radius of 10 cm, what is the length of an arc that subtends a central angle of 60 degrees?

Back

Using the formula L = r * θ (in radians), first convert 60 degrees to radians: 60 × (π/180) = π/3. Then, L = 10 * (π/3) = 10π/3 cm.

Front

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

Back

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

Front

What is the definition of a chord in a circle?

Back

A chord is a line segment whose endpoints lie on the circumference of the circle.

Front

What is the relationship between the diameter and the radius of a circle?

Back

The diameter of a circle is twice the length of the radius. It can be expressed as: diameter = 2 * radius.

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.