Circles - Central Angles, Inscribed Angles, and Inscribed Quads

Front

What is a central angle of a circle?

Back

An angle whose vertex is at the center of the circle and whose sides pass through two points on the circumference of the circle.

Front

What is the measure of a central angle that intercepts a semicircle?

Back

180 degrees.

Front

What is the sum of the opposite angles in an inscribed quadrilateral?

Back

180 degrees.

Front

What is an inscribed angle of a circle?

Back

An inscribed angle of a circle is an angle formed by two chords of the circle that have a common endpoint on the circle.

Front

What is the relationship between the length of a chord and the distance from its midpoint to the center of the circle?

Back

Half the length of the chord.

Front

What is the definition of an inscribed quadrilateral?

Back

A quadrilateral where all four vertices lie on the circumference of a circle.

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 relationship between a central angle and an inscribed angle that intercept the same arc?

Back

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

Front

What is the formula for the length of a chord in a circle?

Back

Length of chord = 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 radius in relation to a central angle?

Back

The radius is the line segment from the center of the circle to any point on the circumference, and it helps define the central angle.