Exploring Central and Inscribed Angles

This video tutorial covers central and inscribed angles in circles. Central angles have their vertex at the circle's center, and their arc measure equals the angle measure. Inscribed angles have their vertex on the circle, and their measure is half of the intercepted arc. Examples demonstrate these concepts, including inscribed angles in semicircles, which always form right angles.

What defines a central angle in a circle?

• An angle with its vertex on the circle

• An angle formed by two tangents to the circle

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

• An angle with its vertex outside the circle

How is the measure of a central angle related to its intercepted arc?

• It is equal to the measure of the arc

• It is half the measure of the arc

• There is no relation

• It is twice the measure of the arc

What is an inscribed angle?

• An angle formed by two radii

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

• An angle formed outside the circle

• An angle whose vertex is on the circle and sides contain chords

How do you find the measure of an inscribed angle?

• Multiply the intercepted arc by 2

• It is equal to the intercepted arc

• Divide the intercepted arc by 2

• There is no specific method

If the arc intercepted by an inscribed angle is 142 degrees, what is the angle's measure?

• 360 degrees

• 142 degrees

• 284 degrees

• 71 degrees

What property does an inscribed angle exhibit when its sides contain chords of the circle?

• Its measure is one-half the intercepted arc

• Its measure has no relation to the intercepted arc

• Its measure is twice the intercepted arc

• Its measure is equal to the intercepted arc

If a central angle measures 82 degrees, what is the measure of the arc it intercepts?

• 41 degrees

• There is not enough information

• 164 degrees

• 82 degrees

For an inscribed angle intercepting an arc of 82 degrees, what is its measure?

• There is not enough information

• 164 degrees

• 82 degrees

• 41 degrees

What is the measure of an angle inscribed in a semicircle?

• 360 degrees

• 90 degrees

• 180 degrees

• 45 degrees

Why is an angle inscribed in a semicircle always a right angle?

• Because it intercepts an arc of 180 degrees

• Because it is formed by two radii

• Because it intercepts an arc of 90 degrees

• Because it is defined by the circle's diameter