Arcs & Sector Area of Circles

Front

What is a tangent line in relation to a circle?

Back

A tangent line is a straight line that touches the circle at exactly one point and does not cross the circle.

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 the area of a sector of a circle?

Back

The area of a sector can be calculated using the formula: Area = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

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

Back

A minor arc is the shorter arc connecting two points on a circle, while a major arc is the longer arc connecting the same two points.

Front

If the radius of a circle is 5, what is the circumference?

Back

The circumference can be calculated using the formula: C = 2πr. For r = 5, C = 10π.

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

How do you find the measure of a minor arc given its endpoints?

Back

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

Front

What is the measure of a major arc if the minor arc measures 170 degrees?

Back

The measure of the major arc is 360 degrees minus the measure of the minor arc. So, 360 - 170 = 190 degrees.

Front

What is the formula for finding the length of an arc in terms of π?

Back

Arc Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

What is the significance of the central angle in determining the area of a sector?

Back

The central angle determines the proportion of the circle that the sector occupies, affecting the area calculation.