Arcs & Sectors

Flashcards based on the concepts of arcs, sectors, and their properties.

What is a central angle in a circle?

A central angle is an angle formed by two radii with the vertex at the center of the circle.

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

A central angle and its intercepted minor arc have equal measure.

What defines a minor arc?

A minor arc of a circle is an arc that is smaller than a semicircle.

How is arc length calculated?

Arc length is the product of the ratio of the central angle in degrees to 360 and the circumference of the circle.

What is the formula for the area of a sector?

The area of a sector is A = (n/360) * πr², where n is the measure of the intercepted arc.

What is the arc length formula in radians?

Arc length (s) = r * θ, where θ is the central angle in radians.

What is a major arc?

A major arc of a circle is an arc that is larger than a semicircle.

How do you find the area of a segment of a circle?

The area of a segment is the area of the sector minus the area of the triangle formed by the endpoints of the arc and the center.

What is the connection between congruent central angles and arcs?

Congruent central angles intercept congruent arcs, and congruent arcs are intercepted by congruent central angles.

To find areas of triangles in circles, what may you need to use?

You may need to apply trigonometric ratios to find the base and height.