Angles of Circles

Front

What is the definition of an angle in a circle?

Back

An angle in a circle is formed by two rays (sides of the angle) that share a common endpoint (the vertex) and are positioned at the center of the circle.

Front

What is the measure of a full circle in degrees?

Back

360 degrees.

Front

What is the relationship between the central angle and the arc it subtends?

Back

The measure of the central angle is equal to the measure of the arc it subtends.

Front

What is the formula to find the measure of an inscribed angle?

Back

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

Front

If the measure of arc AB is 68°, what is the measure of the inscribed angle ACB?

Back

34° (half of 68°).

Front

What is a chord in a circle?

Back

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

Front

What is the relationship between a tangent and a radius at the point of contact?

Back

A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Front

What is the definition of a sector in a circle?

Back

A sector is a region enclosed by two radii and the arc between them.

Front

How do you calculate the area of a sector?

Back

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

Front

What is the definition of a semicircle?

Back

A semicircle is half of a circle, formed by a diameter and the arc connecting its endpoints.