Circle Basics, Central Angles, and Arcs.

Front

What is a chord in a circle?

Back

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

Front

What is the measure of a central angle?

Back

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

Front

How do you calculate the length of an arc?

Back

The length of an arc can be calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

What is the formula for the area of a circle?

Back

The area of a circle is given by the formula: \( A = \pi r^2 \), where \( r \) is the radius.

Front

What is a secant line?

Back

A secant line is a line that intersects a circle at two points.

Front

What is a tangent line?

Back

A tangent line is a line that touches a circle at exactly one point.

Front

What is the relationship between the central angle and the arc it subtends?

Back

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

Front

How do you find the area of a sector?

Back

The area of a sector can be calculated using the formula: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is given by the formula: \( C = 2\pi r \), where \( r \) is the radius.

Front

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

Back

Using the formula \( C = 2\pi r \), the circumference is \( C = 2\pi(10) = 20\pi \approx 62.83 \text{ cm} \).