Angles in 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 drawn from the center of the circle to the circumference.

Front

What is the measure of a central angle?

Back

The measure of a central angle is equal to the measure of the arc that it intercepts.

Front

How do you find the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the arc that it intercepts.

Front

What is the relationship between angles formed by intersecting chords?

Back

The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Front

What is the formula for the measure of an angle formed by a tangent and a chord?

Back

The measure of the angle formed by a tangent and a chord through the point of contact is equal to half the measure of the intercepted arc.

Front

What is the definition of a semicircle?

Back

A semicircle is an arc that represents half of a circle, measuring 180 degrees.

Front

How do you calculate the measure of an arc?

Back

The measure of an arc can be calculated using the formula: m(arc) = m(central angle).

Front

What is the relationship between the angles in a cyclic quadrilateral?

Back

In a cyclic quadrilateral, the opposite angles are supplementary, meaning they add up to 180 degrees.

Front

What is the definition of a chord?

Back

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

Front

What is the relationship between the radius and the angle subtended at the center?

Back

The larger the angle subtended at the center of the circle, the longer the arc it intercepts.