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 such that they extend from the center of the circle to the circumference.

Front

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

Back

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

Front

How do you calculate the measure of an inscribed angle?

Back

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

Front

What is the formula for the circumference of a circle?

Back

The circumference (C) of a circle is calculated using the formula C = 2πr, where r is the radius.

Front

What is the formula for the area of a circle?

Back

The area (A) of a circle is calculated using the formula A = πr², where r is the radius.

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180 degrees.

Front

What is the relationship between the angles formed by two intersecting chords in a circle?

Back

The measure of the 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 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 tangent to a circle?

Back

A tangent to a circle is a line that touches the circle at exactly one point and is perpendicular to the radius at that point.

Front

How do you find the measure of an exterior angle formed by two secants?

Back

The measure of an exterior angle formed by two secants is equal to half the difference of the measures of the intercepted arcs.