Arcs and Angles in Circles

Front

What is the definition of an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

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 calculate the measure of an inscribed angle?

Back

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

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius of the circle.

Front

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

Back

Circumference = 2π(10) = 20π cm.

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180 degrees.

Front

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

Back

Area of a sector = (θ/360) × πr², where θ is the central angle in degrees.

Front

If the central angle of a sector is 90 degrees and the radius is 4 cm, what is the area of the sector?

Back

Area = (90/360) × π(4)² = (1/4) × 16π = 4π cm².

Front

What is the definition of a chord in a circle?

Back

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

Front

How do you find the length of a chord given the radius and the angle subtended at the center?

Back

Length of chord = 2r sin(θ/2), where r is the radius and θ is the central angle.