Understanding Angles in a Circle

The video tutorial explains two types of angles in a circle: central and inscribed angles. A central angle has its vertex at the circle's center, while an inscribed angle has its vertex on the circumference. The inscribed angle is half the central angle subtending the same arc. A special case is discussed where the diameter forms a straight angle, leading to a right inscribed angle. The tutorial also covers solving problems involving these angles, using given circle area and angle measures to find arc lengths.

What is a central angle?

• An angle with its vertex at the center of the circle

• An angle with its vertex on the circumference

• An angle that measures 90 degrees

• An angle that measures 180 degrees

Where is the vertex of an inscribed angle located?

• Outside the circle

• On the circumference of the circle

• At the center of the circle

• Inside the circle but not at the center

How is an inscribed angle related to the central angle subtending the same arc?

• It is unrelated to the central angle

• It is equal to the central angle

• It is half the central angle

• It is twice the central angle

If a central angle measures 80 degrees, what is the measure of the inscribed angle subtending the same arc?

• 80 degrees

• 40 degrees

• 20 degrees

• 160 degrees

In the special case where PQ is a diameter, what is the measure of the inscribed angle PRQ?

• 180 degrees

• 90 degrees

• 45 degrees

• 60 degrees

What is the measure of a straight angle?

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

What is the first step in finding the length of an arc?

• Determine the central angle

• Calculate the radius

• Find the diameter

• Measure the circumference

If the inscribed angle is 30 degrees, what is the central angle subtending the same arc?

• 90 degrees

• 15 degrees

• 30 degrees

• 60 degrees

Given the area of a circle is 9π, what is the radius?

• 4 cm

• 3 cm

• 2 cm

• 1 cm

What is the length of arc ACB if the central angle is 60 degrees and the radius is 3 cm?

• 3π cm

• 2π cm

• 4π cm

• π cm