Central and Inscribed Angles

Front

What is a central angle in a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circumference.

Front

What is an inscribed angle in a circle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle.

Front

What is the relationship between a central angle and an inscribed angle that subtend the same arc?

Back

The central angle is twice the measure of the inscribed angle.

Front

What is a radius of a circle?

Back

A radius is a line segment from the center of the circle to any point on its circumference.

Front

What is a chord in a circle?

Back

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

Front

How do you identify a radius in a diagram of a circle?

Back

A radius can be identified as a line segment that connects the center of the circle to any point on the circle.

Front

What is the measure of an inscribed angle if the central angle is 50 degrees?

Back

The measure of the inscribed angle would be 25 degrees.

Front

What is the formula for finding the length of a chord given the radius and the angle subtended at the center?

Back

The length of the chord can be calculated using the formula: L = 2 * r * sin(θ/2), where r is the radius and θ is the central angle in radians.

Front

What is the significance of the vertex of an inscribed angle?

Back

The vertex of an inscribed angle is located on the circumference of the circle, which is crucial for determining the angle's measure.

Front

What is the difference between a radius and a diameter?

Back

A radius is half the length of a diameter; the diameter is a line segment that passes through the center of the circle and connects two points on the circumference.