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

A central angle is equal to the measure of the arc it intercepts.

Front

What is the relationship between inscribed angles and central angles?

Back

An inscribed angle is half the measure of the central angle that intercepts the same arc.

Front

What is the formula for the circumference of a circle?

Back

C = 2πr, where r is the radius of the circle.

Front

What is the equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r².

Front

If two chords intersect inside a circle, how do you find the measure of the angles formed?

Back

The measure of each angle 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 relationship between the angles formed by two intersecting chords?

Back

The measure of the angle formed by two intersecting chords is equal to the average of the measures of the arcs intercepted by the angle.

Front

What is the measure of an exterior angle formed by two secants?

Back

The measure of the exterior angle is equal to half the difference of the measures of the intercepted arcs.

Front

What is the definition of a secant line?

Back

A secant line is a line that intersects a circle at two points.